Cleary, who scored his team-leading 16th goal on Sunday, was injured in the third period when a shot by teammate Brad Stuart hit his left ankle.
Unaware of the extent of the injury, Cleary returned to the ice during a later power play.
"I was hoping [it was] a bad bruise," he told reporters.
"I didn't know what was going on," Cleary said. "Sometimes in the boot, it can stay. It was sore, but -- I knew after the game, something was wrong."
X-rays showed Cleary had suffered a non-displaced fracture that won't require surgery, but will take him out of the lineup. He believes he will be out at least a month.
"I'm really upset about it," Cleary told reporters. "I don't know what to say. No bright side. Just, four or five weeks, make sure I get back to playing the way I was, that'll be the goal."
Cleary's fractured ankle is the latest in a rash of injuries for the Red Wings, who are already missing centers Pavel Datsyuk and Mike Modano. Datsyuk is expected to be out through January with fractures in his hand and wrist, while Modano is hoping for a March return from a severed wrist tendon.
Despite the injuries and recent struggles that have seen them lose three of their last five games, the Red Wings have held onto the top spot in the Western Conference.
"I don't think [Cleary] really maybe gets the credit he deserves," teammate Niklas Kronwall said, according to the Detroit Free Press. "He's doing a really, really good job for us, and I think he's been one of our most important guys so far. He's one of our leaders. It's tough to lose him."
Detroit has called up forward Jan Mursak from Grand Rapids of the AHL for Monday's game at Colorado.