Minnesota State Statute 609.165
RESTORATION OF CIVIL RIGHTS; POSSESSION OF FIREARMS.
Subdivision 1. Restoration. When a person has been deprived of civil rights by reason of conviction of a crime and is thereafter discharged, such discharge shall restore the person to all civil rights and to full citizenship, with full right to vote and hold office, the same as if such conviction had not taken place, and the order of discharge shall so provide.
If an ex-felon is officially "off-paper," YES. If an offender is still fulfilling the requirements of their sentence (probation, parole, anything else included in the sentence), NO.
Once you are off paper (check with your p.o. or county to make sure), you can register to vote, as long as you are otherwise eligible. If you are not yet "off paper," it is a felony to register to vote.
Please see the following links:
https://www.revisor.leg.state.mn.us/statutes/?id=609.165
http://www.sos.state.mn.us/home/index.asp?page=4
www.mncn.org/mpp/doc/exfelons.pdf
http://www.sos.state.mn.us/home/index.asp?page=520