The Gemara (Nidda 61b) cites R' Yosef, that מצות בטילות לעתיד לבא.
בגד שאבד בו כלאים הרי זה לא ימכרנו לעובד כוכבים ולא יעשנו מרדעת לחמור
אבל עושה ממנו תכריכין למת. אמר רב יוסף
זאת אומרת מצות בטלות לעתיד לבא
On the other hand, one of the 13 Principles of Faith proclaim our unwavering belief that 'זאת התורה, לא תהא נחלפת ולא תהא תורה אחרת' - The Torah in the form that we have it is complete, and will never be changed or replaced ever.
There are numerous methods in the Rishonim how to explain that statement of R' Yosef in Nidda - how literally to take it, and which period in the future it is discussing.
Tosfos (Nidda 61b) - it is referring to the period of Techias
Hameisim; אין בין .העולם הזה לימות המשיח אלא שעבוד מלכויות בלבד
Rashba (ibid, Berachos 12a) - there will never be a period where
the Torah is not exactly as we have it. The Gemara means that dead
people are not obligated in mitzvos while in the grave. (This seems to be the opinion of the Rambam [Kilayim 10.25].)
Ritva (explained in Kovetz Shiurim V2 §28(?)) - there is no
specific period where the Torah will not be relevant; rather, death
removes the obligation of mitzvos from a person, even if after
Resurrection. (If one were to die now and be resurrected, the same
law would apply)
Maharitz Chiyas (Nidda 67b) - this is a temporary dispensation for the
momentary event of Resurrection, but immediately thereafter the
Mitzvos will return as we have them. (It will be a 'הוראת שעה')
(5. Ramban (Devarim, 30:6) - it is referring to the Yemois
Hamoshiach. The Ramban does not refer directly to our Gemara, although he discusses the idea of mitzvos and aveiros not existing after Yemois Hamoshiach, due to lack of yezter hara.)
The Sdei Chemed (מערכת המ' כלל רי"ח) quotes Nachlas Binyamin and Noam Megadim that only negative commandments (מצוות לא תעשה) will become permitted, but positive obligations (מצוות עשה) will always continue.
Others (בקונטרס דברי חכמים סימן נ"ג) say the oposite; negative commandments will stay, but the positive commandments will become obsolete. The Yaa
Yaaros Devash (ח"ב דף נ"א) says that all mitzvos will remain, but in the form of אינו מצווה ועושה - voluntary commandments rather than obligatory.
According to the opinions of the Rashba, Rambam, and Maharitz Chijas (cited earlier), no mitzvas will become obsolete.
According to the Ritva, it will only be from those who had previously died and were Resurrected. According to the other opinions, even those still alive will be included in this halacha.
[There are numerous Gemaras which support that during the Days of Mashiach, the obligations will still be relevant. (See Beitza 5 - שמא יבנה המקדש מיד חיישינן. Talmudic sources also write that we will give Terumah to Ahron HaKohen after he is resurrected, alluding to the continuity of Mitzvos Teruma and Kehuna. See also Zevachim 45 הלכתא למשיחא, with Keren Orah.]