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.

My fish's native habitat is rice fields.

To make it sound more natural, you could reverse the order thus:

Rice fields are my fish's native habitat.


Please advise, but Grammar Girl opines that the problem here is 'false attraction to a predicate noun'. I excerpt the fundaments:

Although this problem may seem complicated, it’s really not. It’s as simple as this: the verb agrees with the subject (2)1, not the predicate noun. - See more at: Verbs sandwiched between singular and plural nouns - Quick & Dirty Tips

Dorothy, don’t pay attention to the man behind the curtain, meaning don’t be distracted by the predicate noun. One grammar source calls this problem “false attraction to a predicate noun” (3). - See more at Quick & Dirty Tips

1. The (2) and (3) refer to external references on p 2 of 2 of Grammar Girl's article.