No.
Both wav and mp3 files are audio files. Neither file format includes any MIDI data.
More generally: I think you're confusing yourself with the notion of "hearing" a MIDI track. To be accurate, you can't hear a MIDI track: you can only hear a synth playing a MIDI track. Here's an analogy: you can't hear a text file, or a book, either. You need someone to read it out loud.
If you're using DAW software, and you have a MIDI track in there that you're hearing, that's because you're having some synth (most likely your computer itself, playing a virtual instrument) playing it. You can certainly export that audio into a wav or mp3 file - either as a part of a mix or as a separate track.