Cleary will need surgery on a broken jaw suffered in Saturday's 3-2 overtime loss against Toronto and will be out six to eight weeks, according to The Sports Network of Canada. He was hit in the face by the puck in the first period.
Cleary, who is tied for third on the team in scoring with 20 goals, has not missed a game all season.
"He's been playing real well for us," Lidstrom told the Detroit Free Press. "He is one of our key players on the power play on the second unit, and I think he's been coming along real well, hanging on to the puck and making plays.
"He's so good down low at hanging on to the puck and making plays with it, so someone has to step up and replace him."
Information from The Associated Press contributed to this story.