Shaw scored a goal on his lone shot in Tuesday's 3-2 win over the Senators.
Shaw signed a one-year, two-way contract Thursday.
Shaw (knee) wasn't qualified Friday and will become an unrestricted free agent, Jessi Pierce of NHL.com reports.
Shaw (knee) will miss the rest of the regular season and the playoffs, Dane Mizutani of the St. Paul Pioneer Press reports.
Shaw (suspension) will return to the lineup against St. Louis on Saturday, Michael Russo of The Athletic reports.
Shaw received a two-game suspension for kneeing Evgeny Svechnikov on Thursday.
Shaw will have a hearing with the NHL Department of Player Safety for kneeing Evgeny Svechnikov on Thursday.
Shaw scored a goal and registered an assist in Minnesota's 5-3 loss to Calgary on Wednesday.
Shaw notched a goal on three shots in the Wild's 6-1 blowout victory against the Jets on Wednesday.
Shaw scored his second career goal during a 4-1 win over the Canadiens on Tuesday.