This site doesn't provide practical answers to real questions. As such the below is written to illustrate the reasoning a rabbi might use to come to a decision. Small changes in the question can impact the answer significantly so be sure to ask a rabbi if this is relevant in practice.
This is actually a quite complicated question which I researched for a long time because of 3 separate issues
- Is one allowed to open a package on Shabbat when it is not food or medicine?
- In what case is one allowed to tear a cover with writing on it if one risks tearing the writing (as I understand that contact lenses packages often have writing on the back, see e.g., here or here)?
- Is wearing contact lenses a Shabbat need or mere convenience? (and this might depend whether the person wouldn't see without contact lenses or has an alternative like regular glasses)
In general, it is forbidden on Shabbat to tear apart glued items (koreya), demolishing a utensil (soteir) and tearing apart writing (mocheik) - see e.g., here.
Here is what I think the halacha would be
- there is no question that, in case of medical need (here as a bandage to the eye), one can open a glued package, break a utensil and (if there is no other way) tear apart the writing on the package, see e.g., here and below
- for non-medical needs, it appears to depend on whether wearing contacts is a "Shabbat need" for that particular person. In discussions with contact lens wearers, I learned some absolutely require them (either because they don't have or like regular glasses) in which case it would be permitted while for others in it a total convenience. Some rabbis I spoke with recommended opening the package with a shinui, a departure from the normal practice, e.g., with the teeth, especially if there is writing on the package
See below for details and reasoning
One of the 39 forbidden actions on Shabbat is tearing (koraya). It is in general permitted to tear open packages of food (while being careful not to tear lettering on the package, and in some cases not to create a vessel) but forbidden to do so for non-food items.
In the case of glued items, R Dovid Ribiat, the author of an encyclopedia on the 39 forbidden actions (The 39 melochos, vol. 3, p. 830) writes
[...] all poskim [halachic decisors] agree that pulling apart any two
objects that are glued together (regardless of what material they are
made of) at their point of attachment is the melocho [forbidden
action] of koraya [tearing]
However, beyond the exception for food, there are also exceptions for medical needs. As such it is permitted to open band aids on Shabbat even when their protective paper is glued (R Ribiat p. 848, see bottom of here), one may tear the wrapping around a pill (Shmirat Shabat Kehilchata 33:4) and around a dressing (Shmirat Shabat Kehilchata 35:20). In all cases this is provided one doesn't tear the lettering if there is one.
R Simcha Bunim Cohen writes similarly in Sanctity of Shabbos (vol. 1, p. 83-86) that
if a package is glued shut, one may not tear it open - even in a
manner that destroys the wrapping except in cases of food or
medicine [...] The dispensation applies only for obtaining items of
true necessity such as food or medicine. It is forbidden to tear
destructively in order to obtain an item that is a mere convenience
The best summary of the entire issue with many detailed sources comes from R Akiva Niehaus (here)
Harav S.Z. Auerbach zt”l holds that one may open non-food packages on
Shabbos in a destructive manner provided that it is a tzorech Shabbos,
but the Mishna Brurah (according to one explanation) holds that one
may not open a non-food package on Shabbos. Since the Mishna Brurah’s
position is questionable, one may rely on the lenient opinion of Harav
S.Z. Auerbach zt”l. However, the classification of “tzorech Shabbos”
is quite vague and every case requires clarification if it is truly a
tzorech Shabbos
Two rabbis I discussed it with allowed opening such a package if they are considered a Shabbat need and of course if they are a form of bandage for the cornea.