The big left-hander suffered a Grade 2 strain while pushing off the rubber in Tuesday's 3-2 loss to the Los Angeles Angels in Anaheim.
It could be a big loss for the Yankees, who were seeing the left-hander pitch like an ace again in his past six starts (0.99 ERA).
Grade 2 hamstring strains can take four to eight weeks to fully recover. Though normally associated with runners, they also can be a difficult challenge for pitchers, Yankees manager Joe Girardi said
"It can be an issue when it's a push-off leg,'' Girardi said. "That's the leg you're using to drive downhill and push off on.''
New York recalled right-hander Domingo German from Triple-A Scranton/Wilkes-Barre to take Sabathia's roster spot and also brought up right-hander Luis Cessa from Triple-A. Cessa might start Saturday or Sunday against the Oakland Athletics.
The Associated Press contributed to this report.