The Dutch international suffered the injury trying to keep out Carlos Tevez's winner just after the hour.
He was replaced by Gerhard Tremmel in what was his second Premier League appearance.
"It's a big blow for us because Michel is a very good goalkeeper who has been playing well," Swansea manager Michael Laudrup told the club's website.
"But that is part of football.
"When you have lots of games you are always going to get injuries and suspensions."
- Sports & Recreation
- Gerhard Tremmel
- Carlos Tevez