Cleary has one goal and two assists in 18 games but just one point in the past 12, and Red Wings coach Mike Babcock said he hopes the time off helps Cleary rediscover his game.
"My job each and every day is to put the best 20 guys in the lineup that I think can help us win today," Babcock told reporters. "I've been with [Cleary] for nine years. I know him well; there's no one who's a bigger fan of Dan Cleary than Mike Babcock.
"I imagine he's very [angry] today and I don't know what you want me to do about it."
Cleary said he plans on using his benching as a motivating tool to get better.
"I've just got to work hard, stay positive and be professional about it," he said. "There's a lot of hockey left.
"Frustrating is normal. You can't dwell on the negatives, you have to be positive, you have to work hard. That's it."
"So there would be no need to make any kind of lineup change there," Jets coach Claude Noel told reporters in Detroit. "It doesn't always revolve around winning because some people say don't change a winning lineup and I'm not one of those that believe that so much. But if they play well, that's great. And I feel we have played well."
Here is how the teams could look Tuesday:
Scratched: Anthony Peluso