There are really two problems in answering this question, both revolving around the respective powers of the things in question. Superman as he was originally conceived would almost certainly be destroyed by a nuclear weapon, rectally inserted or not. The Death of Superman saw him killed by the immensely powerful Doomsday, but the hits he sustained in that were by no means the equivalent of nuclear detonations.

Some variations of him, on the other hand, have him be pretty much explicitly invincible, unless exposed to Kryptonite or magic. If such an iteration is used, presumably the forces unleashed would expel themselves as a tremendous nuclear fart that rockets him off into space, but he could fly back under his own power.

The bomb itself is the other half of the question. Nuclear devices have no theoretical upper limit, rather they are bounded by technical construction considerations, cost, and the ability to secure sufficient nuclear material. Though devastating, the bombs dropped in WW2 were absolutely puny compared to today's - the bigger of the two, Fat Man, was about 20 to 22 kilotonnes in yield. Today's strongest in-service US weapon is the B83, which has a variable yield that tops out at 1,200 KT, or 1.2 megatonnes - almost 550 times more powerful than Fat Man.

The most powerful nuclear weapon ever detonated was the Soviet Tsar Bomba, which was detonated over Novaya Zemlaya. It had a yield of approximately 50 MT, which was constrained because they deliberately constructed part of it to do so. Had they gone for the maximum possible yield of the weapon it would have been about 100MT (this involved which elements were used for certain interior parts).

In the lower yields, it's pretty plausible that Supes would survive a nearby nuclear detonation, but maybe not when actually inside his colon. In the higher yields - we'll assume his body can handle the stretching this would entail, by the way, because we're not playing FATAL so we do not have and do not want the means to calculate the elasticity of someone's rectum - we have to assume that he would be annihilated, except in the instances where he is all but explicitly invulnerable.

So combine the two together and what do we find? Well, at lower yields, with tougher iterations of Superman, you can convince me he would survive. If Superman is in one of his weaker instances, or he is unfortunate enough to be the victim of a multi-megaton anal detonation (though to be fair many of us survive Montezuma's Revenge after cheap Mexican food ) then it's pretty certain that he is toast.

One element, if you'll pardon the pun, remains unaccounted for. Kryptonite is explicitly a radioactive element (that's why his Kryptonite ring gave Lex Luthor cancer). This fact is not, by itself, sufficient for a nuclear device - but if it, or an isotope thereof, does meet the criteria needed for such uses, we can pretty safely say that any version of Superman would be destroyed utterly by even the mildest of Kryptonite-based fission or fusion bombs.