The 30-year-old Markov, signed as a free agent during the summer, has been a key player for Detroit this season.
Paired with Nicklas Lidstrom, Markov has a goal and six assists for seven points and is plus-13 in 25 games. He plays an average of 18 minutes, is one of Detroit's top penalty-killers and has provided a needed physical presence.
"Obviously he's played very well for us and has been a good partner for Nicklas Lidstrom," said Red Wings general manager Ken Holland. "Obviously a big loss, but we've got other defensemen we think can step up."
The Red Wings, who also have defenseman Niklas Kronwall out of the lineup with a sore groin, recalled defenseman Derek Meech from AHL Grand Rapids.
Markov has a history of injuries. In eight full NHL seasons he's played more than 60 games twice.