Franzen was injured in Thursday night's 3-2 victory over the Chicago Blackhawks, a game in which Franzen scored the game-winning goal during the second period.
"It's a huge impact because he's a huge player for us," Red Wings coach Mike Babcock told ESPN.com's Pierre LeBrun on Friday. "But like I always say when things don't look good, we just have to find a way. Somebody will get an opportunity now."
It wasn't clear from the Wings' announcement at what point in the game Franzen was hurt.
Franzen, a native of Vetlanda, Sweden, was Detroit's second-leading scorer last season with 34 goals as the Wings' back-to-back Stanley Cup bid was thwarted in seven games by the Pittsburgh Penguins. Right winger Marian Hossa had 40 goals.
Franzen, 29, a third-round pick by Detroit in 2004, has 84 goals and 61 assists in four-plus NHL seasons with the Wings.