Detroit made the move Monday, keeping the veteran defenceman out of the lineup for a minimum of 10 games.
Kronwall has not played since Jan. 17 against Philadelphia and missed four games before the All-Star break. He will be eligible to return Feb. 14 against Boston. He has scored three goals, 17 points and has a career-worst negative 10 plus-minus rating.
The Red Wings play at Tampa Bay on Wednesday night.