The sentence could be considered as ambiguous, but:
The three-word sentence "X invited Y." doesn't convey much meaning, unless you already know something about the invitation.
Giving more information about Y (for example "X invited Y who lives in New York.") doesn't change that situation - without more context about the invitation, we still don't know what is going on here.
So in the OP's sentence, it is more reasonable to interpret the words "next door" as telling us more about the invitation, rather than telling us more about Mickey.
There is nothing at all in the sentence that suggests "invited" means "invited to Minnie's house", but presumably the reader already knows that Mickey and Minnie live next door to each other, and it wouldn't make much sense for Minnie to invite Mickey either to "the other house that is next door to Minnie's house" (on the opposite side to where Mickey lives) or to "the other house that is next door to Mickey's house" (on the opposite side to where Minnie lives).