Mirror neurons themselves were never parapsychology, but they explain phenomena that were considered paranormal before their discovery:

http://health.howstuffworks.com/synesthesia.htm/printable

Hold on. This is a historical question; electromagnetism explains stuff that could be considered paranormal as well, but that stuff wasn't. Were the mirror neuron phenomena actually noticed, classified under parapsychology, and investigated by parapsychologists, producing results that had any connection to their eventual uptake by mainstream psychology/neurology?

The link doesn't mention anything like that; if anything, the example of the woman who thought mirror-touching was perfectly normal & universal suggests the opposite.

No, I strongly doubt Rizzolatti and his colleagues considered their discovery to be parapsychology.