My fish's native habitat is rice fields.
My fish's native habitat are rice fields.
I'm pretty sure the first is correct, since 'is' modifies 'habitat,' but it still sounds weird...
It may sound weird, but it is still correct. Singular nouns take singular verbs. In this case, the singular noun is habitat. Thus, is is the correct form of the verb to be in this case.
To make it sound more natural, you could reverse the order thus:
Please advise, but Grammar Girl opines that the problem here is 'false attraction to a predicate noun'. I excerpt the fundaments:
***The (2) and (3) refer to external references on p 2 of 2 of Grammar Girl's article.