Gemara

Mishnah: R. Yehudah requires a Mezuzah for a Sukah during Sukos; Chachamim exempt.

Beraisa: R. Yehudah says that a Sukah must Me'arev with the Chatzer (or else it forbids the others from carrying). It needs a Mezuzah, and it is Kove'a for Ma'aser (Tevel may not be eaten Arai once it entered a Sukah, as if it entered a house).

Suggestion: Perhaps this is mid'Rabanan.

Rejection: (Surely, all of these have the same status.) Granted, we could say that the obligations to Me'arev and have a Mezuzah are mid'Rabanan - but Chachamim would not obligate Ma'aser mid'Rabanan, lest one declare produce that is exempt (mid'Oraisa) to be Ma'aser on produce that is liable, or vice-versa (such a separation is invalid)!

Abaye: All require a Mezuzah during the seven days (of seclusion of the Kohen Gadol, just like it is required during Sukos); they argue about the rest of the year. Chachamim decree about the rest of the year on account of the seven days; R. Yehudah does not decree.

Objection (Rava): The Beraisa says that they argue about during Sukos!

Rava: Rather, R. Yehudah requires a Sukah to be Diras Keva, therefore he obligates a Mezuzah; Chachamim require Sukah to be Diras Arai, therefore they exempt from Mezuzah.

Rishonim

Rambam (Hilchos Mezuzah 6:9): A Sukah for the Mitzvah during Sukos is exempt from a Mezuzah, since it is not Diras Keva.

Kesef Mishneh: All exempt a Sukah the rest of the year. They only argue about during Sukos. Chachamim exempt because Sukah is Diras Arai, and only Diras Keva requires a Mezuzah.

Bach (OC 286 DH Sukas): We know from elsewhere that they argue about Diras Keva; this is why Chachamim disqualify a Sukah above 20 Amos, and R. Yehudah allows it.

Tosfos (Sukah 7b DH Acherim): 'Acherim', i.e. R. Meir, requires Diras Keva. On 8b, R. Meir exempts Sukas Yotzrim from a Mezuzah. We must say that he refers to the rest of the year, for in Yoma (10a) we find that R. Yehudah obligates Sukah in Mezuzah during the Chag because he requires Diras Keva.

Question: Perhaps the other Tana'im who require Diras Keva (in other respects) do not require as much Keva as R. Yehudah, therefore they exempt from Mezuzah!

Answer (Tosfos Yeshanim 10b DH v'R. Yehudah): The Gemara (Sukah 21b) says that R. Yehudah and R. Shimon both require Diras Keva; they argue about whether or not an Ohel Arai is Mevatel an Ohel Keva. It did not say that R. Shimon does not require as much Keva as R. Yehudah, and he holds that (regarding Ohel Mevatel Ohel) that the Ohel of Sukah is also considered Arai!

Note: We can give a second answer according to Tosfos ha'Rosh (Sukah 7b DH Kulhu), i.e. that the other Tana'im require Diras Keva more than R. Yehudah. Tosfos ha'Rosh explains that R. Yehudah allows a Sukah to be Keva, but he also allows Diras Arai. This suffices to show that he considers the Ohel of Sukah to be Keva. R. Shimon requires a Sukah to be Kavu'a, all the more so he considers the Ohel of Sukah to be Keva!

Tosfos (Sukah 7b DH Acherim): 'Acherim', i.e. R. Meir, requires Diras Keva. On 8b, R. Meir exempts Sukas Yotzrim from a Mezuzah. We must say that he refers to the rest of the year, for in Yoma (10a) we find that R. Yehudah obligates Sukah in Mezuzah during the Chag because he requires Diras Keva.

Question: Perhaps the other Tana'im who require Diras Keva (in other respects) do not require as much Keva as R. Yehudah, therefore they exempt from Mezuzah!

Answer (Tosfos Yeshanim 10b DH v'R. Yehudah): The Gemara (Sukah 21b) says that R. Yehudah and R. Shimon both require Diras Keva; they argue about whether or not an Ohel Arai is Mevatel an Ohel Keva. It did not say that R. Shimon does not require as much Keva as R. Yehudah, and he holds that (regarding Ohel Mevatel Ohel) that the Ohel of Sukah is also considered Arai!

Note: We can give a second answer according to Tosfos ha'Rosh (Sukah 7b DH Kulhu), i.e. that the other Tana'im require Diras Keva more than R. Yehudah. Tosfos ha'Rosh explains that R. Yehudah allows a Sukah to be Keva, but he also allows Diras Arai. This suffices to show that he considers the Ohel of Sukah to be Keva. R. Shimon requires a Sukah to be Kavu'a, all the more so he considers the Ohel of Sukah to be Keva!

Poskim

Shulchan Aruch (YD 286:11): A Sukah for the Mitzvah during Sukos is exempt.

Source (Beis Yosef DH Sukas): "Beisecha" teaches that only Diras Keva like a house is obligated.

Mishbetzos Zahav (OC 643:4 DH Amar): A Sukah is always exempt from a Mezuzah. Even if one lives in a room all year, and on Sukos he removes the ceiling (and replaces it with Sechach), it is exempt during Sukos, for it is considered Diras Arai.

Mishnah Berurah (660:21): If one has an inner room and an outer room, and one of them was made to be a Sukah:

If the inner room is the Sukah, the opening between the rooms requires a Mezuzah, for it is an opening of the other room;

If the outer room is the Sukah, its opening to Reshus ha'Rabim requires a Mezuzah, for it is like a Beis Sha'ar of the other room.