Bartkowski agreed to a one-year, two-way deal with Minnesota worth $650,000.
Bartkowski tallied an assist and fired six shots on goal in Tuesday's 4-1 loss to the Coyotes.
Bartkowski has been a healthy scratch for 18 of the past 19 games after watching Sunday's 6-1 win from the press box.
Bartkowski has only dressed for three of the past 11 games.
Bartkowski will be a healthy scratch for Saturday's home game against the Wild, Derek Wills of Sportsnet 960 The Fan reports.
Bartkowski received just 11:30 if ice time during Thursday's 2-1 loss to Carolina.
Bartkowski scored his first goal of the season in Saturday's overtime win over the Blues.
Bartkowski agreed to terms on a two-year, two way deal with the Flames on Thursday, Kristen Odland of Postmedia reports.
Bartkowski signed a professional tryout contract with the Flames on Wednesday.
Bartkowski was released from his professional tryout with the Senators on Wednesday, Bruce Garrioch of the Ottawa Sun reports.