I had thought the answer was "absolutely yes" (i.e., you cannot pet even your own dog on Shabbos), but I checked two of my Shabbos seforim and the Internet and found a bit of nuance.
Volume 2, Part V of The Concise Code of Jewish Law: Compiled from the Kitzur Shulhan Aruch and Traditional Sources by Rabbi Gersion Appel says this:
"All animals including pets are muktzeh. Hence it is not permitted to
handle and fondle dogs, cats, and other animals on the Sabbath. It is,
however, permitted to give them food, as indeed it is one's duty to
feed his animals. [...] If the animal is in distress, or it is
necessary to prevent its suffering, one may hold it by the neck and
lead it" (333).
Volume 1 of A Semicha Aid for Learning the Laws of Shabbos: An English Translation and Compilation of the Laws of Shabbos from the Alter Rebbe's Shulchan Aruch, in Accordance to Topic by Rabbi Yaakov Goldstein reiterates that animals, including domestic animals, are muktzeh and cannot be moved on Shabbos; however, in a private domain they can be moved by their neck, their sides, and their legs (without lifting them off the ground) if "the animals need this to be done"; i.e., to prevent suffering (331). In a public domain or a karmalis, one may only push the animal[s] from behind, so as not to come close to carrying. (Interestingly, this source suggests that the specific prohibition of carrying does not apply to non-domestic animals--although they may still be muktzeh, and certainly my first source suggests they are.)
On p. 332, my second source responds thus to the specific question "May one pet his dog?":
"Seemingly this may not be done as one moves its hairs by doing so,
and moving even part of an animal is forbidden unless done to prevent
the animal pain. Perhaps however one can claim that hair is not
considered a real substance as is a limb. Vetzrauch Iyun."
I found another lenient discussion here:
A. Are Pets Muktza? The Talmud (Shabbat 128b) states that animals are
muktza. The reason for this, explains Magid Mishnah41 (commentary to
Rambam Hilchot Shabbat 25:25), is that animal have no utility on
Shabbat and Yom Tov. Hence, they are comparable in this regard to
sticks and stones which are classified as "muktza machamt gufa",
muktza by its very nature (i.e., because they have no utility on
Shabbat and Yom Tov). The Rishonim, however, debate whether an animal
which can be used to quiet a child from crying is considered to be
muktza. Tosafot (Shabbat 45b s.v. hacha), Mordechai (Shabbat 316) and
Hagahot Oshri (commenting on Rosh, Shabbat 3:21) cite authorities who
believe that such animals are not muktza by virtue of the fact that
they have utility. Yet Tosafot, Mordechai, Hagahot Oshri, and Rosh
(cited in the responsa of Maharach Or Zarua, 82) reject these
authorities because of two possible considerations. First, the fact
that an animal can be used to quiet a child from crying is
insufficient utility to render the creature no longer to be considered
muktza machmat gufa. Second, the rabbis classified all animals as
muktza regardless of whether a particular animal has utility on
Shabbat and Yom Tov. This is an example of "lo plug rabbanan",
rabbinic legislation which was instituted for a reason, yet embraces
even the cases for which the reason does not apply Shulchan Aruch
(308:39) appears to accept the position that all animals are
considered to be muktza since Rabbi Karo states that animals are
muktza without exception. Indeed, Shulchan Aruch Harav (308:78) rules
stringently in this regard.43
The question arises, though, whether circumstances have changed since
the time of the Rishonim. These authorities discuss animals which can
possibly be used to amuse children but not animals whose entire
purpose is to entertain and provide companionship to their owners.
Rabbi Shlomo Zalman Auerbach (cited in Shmirat Shabat Kehilchata 27,
footnote 96), in fact, raises the possibility of making this
distinction, yet he rules that pets are muktza. Rabbi Moshe Feinstein
(Iggerot Moshe, Orach Chaim 4:16 and cited in "the halachos of Muktza"
p. 7 of the Hebrew section, paragraph twenty-four) and Rabbi Ovadia
Yosef (Yabia Omer, 5:26) also reject the possibility of making such a
distinction. It appears that this question is contingent on one's
acceptance of one of the two reasons (stated above) offered by the
Rishonim) for why an animal that can be used to quiet a child from
crying is muktza. If one adopts the position that the rabbis have
deemed all animals to be muktza, regardless of their utility, then
even household pets are to be included I this category. However, if
one assumes the position that the possibility of using an animal to
amuse a child is insufficient utility to remove it from being
considered muktza, then a cogent argument can be made that a pet is
sufficiently useful to the extent that one no longer can say that they
have no purpose to their owners on Shabbat and Yom Tov, and hence are
Rabbi Shmuel David (Sheilot uteshuvot Meirosh Tzurim 38:6) concludes
his discussion of this issue with a citation of the opinion of Rabbi
It is proper to conduct himself in accordance with the stringent
opinion in this matter, since this appears to be the opinion of
Tosafot, Mordechai, Hagahot Oshri, and Rosh. Yet one need not admonish
those who practice in accordance with the lenient opinion in this
matter. Since this issue is embroiled in a dispute amongst the
Rishonim and the logic of those who rule leniently is compelling.
However, even according to the stringent opinion it is reasonable to
say that one may move a household pet to alleviate its suffering
(Yabia Omer 5:26). This is because some authorities permit moving
items which are undoubtedly muktza to spare an animal from suffering
(see Mishnah Berurah 305:70 and Chazon Ish 52:16). Since the question
as to whether household pets are muktza, is in dispute, there exists a
s'fek s'feka, a double doubt, which would lead one to rule leniently
in this ragard.45
- This explanation is also cited by Beit Yosef (Orach Chaim 308 s.v. kofin) and Mishnah Berurah (308:146).
- See Tehilla Ledavid 308:42 for a distinction between Kosher and non-kosher animals regarding the category of muktza under which they
should be classified.
- However, see Respnsa halachot Ketanot (number 45) who adopts a lenient position in this matter. Rabbi Shmuel David (Sheilot Uteshuvot
Meirosh Tzurim 38:6) cites Chief Sepharadic Rabbi Mordechai Eliyahu
who rules leniently in this matter since the issue debated by the
Rishonim is a rabbinic law where one may rule leniently in case of
- Rabbi Shmuel David (Sheilot Uteshuvot Meirosh Tzurim) cogently argues that one who is accustomed to move his pets is analogous to
someone who prepares a rock prior to Shabbat for use on Shabbat. In
such cases the rock is no longer muktza since he has demonstrated that
the rock has utility for him on Shabbat (ordinarily, rocks are muktza
since they serve no purpose on Shabbat; once one demonstrated his use
for a rock then it is no longer classified as muktza). Similarly, one
who ordinarily moves his pets demonstrates thereby that they have
utility on Shabbat and hence are not muktza. Rabbi Auerbach (cited in
Shmirat Shabbat Kehilchata 18, footnote 62) rules that seeing-eye dogs
are not muktza. He reasons that since their essential function is such
that they must necessarily be moved, then one surely intends to move
them on Shabbat and hence their designation as muktza is avoided.
Rabbi David points out that a rabbinic authority who rules that a
seeing-eye dog is not muktza would not necessarily rule that a
household pet is not muktza. One can distinguish between seeing-eye
dogs whose function requires their being moved (and hence one surely
intends prior to Shabbat to use them on Shabbat) and household pets
which are ordinarily moved but are not necessarily moved.
- Rabbi Y. Neuwirth rules leniently in this regard, though he expresses some hesitation in doing so; see Shmirat Shabbat Kehilchata
27:28 and 30 and footnote 98.
Another relevant issue might be the prohibition of gozez (shearing), since it may be likely or inevitable that hair is pulled out of the dog in the course of petting. This is just a thought I had, though, and I'm not sure.
Another remaining question, it seems, is to what extent indirect petting of your dog (i.e. with an object) would be a problem.
A personal note: This prohibition initially caused me pain as a dog owner and lover who usually pets her dogs at every opportunity. I quickly learned, however, that some sweet words will readily assuage a dog, and dogs are actually better behaved (read: less spoiled) on the days you don't pet them. Good luck!