No. An MP3 is essentially a compressed wave file, that is, the file contains a description of the sound "wave" that makes up the audio. It is a little more in-depth than that, but that will be sufficient.
A MIDI file, on the other hand, contains a description of which musical instruments are playing what notes at what time.
Converting a wave sound to a MIDI file is essentially the same as listening to a song, then writing down the music on a stave. You could CREATE a midi file of a song using MIDI authoring software, provided you had an ear for the sound and were patient enough to work out how to play it.