Update: The bill has now passed in four different Senate committees. There is now a companion bill in the House, H.F. 293, but that bill has yet to receive a hearing and it is very unlikely to pass the Minnesota House.
The Minnesota Senate Committee on State Government Finance and Policy and Elections held a hearing on S.F. 173 on January 27. Video of the hearing is available here. The bill would require voters to present a photo ID in order to vote and in order to register to vote on election day. Those unable to present the required form of photo ID would be allowed to cast a provisional ballot, but in order for a provisional ballot to be counted, the voter would need to go to their county auditor or municipal clerk's office within seven days and provide the required photo ID or sign an affidavit saying they attempted to and were unable to obtain that ID.
The bill would also eliminate the use of a driver's license with an old address plus a utility bill or other document serving as proof of residence, and would eliminate vouching, as a means of registering to vote on election day. Media coverage mentioning the bill in broad terms is available from the Associated Press, MinnPost here and here, and from WCCO. A press release from the Minnesota Senate Republican Caucus regarding the bill is available here.