I own a Pioneer DV-59AVi which supports the MP3 format, however after copying MP3s onto a DVD-R disc from my computer the Pioneer will not play the music. Is this because the player is designed only to read MP3 formatted music from a CD and not a DVD?

The manual that came with the player should be able to tell you this. It's possible that the player will only recognize DVDs formated as DVDV or DVDA. It would seem strange though, because most of the newer Denon players will read just about any compatible data format off a recorded DVD.

Yep, I would check the manual. I just picked up a cheapo Samsung DVD Recorder and the manual says it will only playback MP3s from CD-R's