Mycroft just hadn't gotten around to putting his clothes on

Digital Spy asked Stephen Fry, who plays Mycroft, about the nakedness in that one scene. Stephen explains (see video at 4:30 onwards):

The idea of this man, who lives alone... and he' forgotten that he's invited Watson's fiancée to come and stay to be safe from the threats of Moriarty and he's so used to living alone and so used to his regular life wandering about that he gets up in the morning completely naked reading a newspaper and there's... this girl completely shocked out of her wits and he just carries on as if nothing's happened...

He forgot that Mary was staying at his house, and never usually has guests

Mycroft lives in splendid isolation, barring his servants who are very elderly and effectively below his notice. He is also a very cerebral man who could overlook the need to get dressed immediately when observing his usual home routine. Naturally Mycroft is fully and smartly dressed when out and about, but clearly almost never has overnight guests at home.

No particular reason

The movie bears little resemblance with Doyle's source material. It also doesn't go into too much detail why Mycroft would be naked.

My interpretation is that the scene is there for comedic relief and to show a bit about their personalities. Mycroft is a relaxed homosexual (or asexual, as commenters have pointed out) who doesn't care much for societal expectations, and Mary is a very conservative woman who is obviously bothered by a random naked man.

Mycroft might be a naturist

While the whole scene is made for comedic effect (aka. "rule of funny"), there is a possible explanation: Mycroft might be a naturist, enjoying non-sexual nudity.

The Wikipedia mentions that the earliest modern naturist club has been created in British India in 1891 - this is more or less the time the Game of shadows takes place¹. Since Mycroft is quite interested in novelties, it is quite possible that he has joined this club, even if only remotely (the exact opposite might be also true - before 1840, public nude swimming was socially acceptable in Great Britain, so Mycroft might be very old fashioned, but it seems too far fetched as Mycroft is not going for a swim).

^{1 - I don't think it has been exactly stated when the movie takes place (but for example the Mayerling Incident from January 1889 is mentioned), but naturism became quite popular in Europe early in the 1900s}

Another option:

Because he can

Do you care if you are walking naked in front of your dog? In his house, there is only his servant, his assistant and a woman. The first two are just a part of the furniture, the last one is...well, just barely a wife to a doctor. Who cares if those lowly creatures see him?