The injury makes the Yankees' slight chance to get to the playoffs even more unlikely.
"We have hopes and beliefs that next year will be a better year for him and for us," general manager Brian Cashman said. "There's no point in having him make his last start with an injury."
Sabathia was supposed to start Wednesday night at Yankee Stadium against the Tampa Bay Rays, one of the four teams the Yankees trail in the AL wild-card hunt.
After losing 2-1 Sunday to the San Francisco Giants, they were four games out of the final AL playoff spot with six games to play. But during the second inning of that game, Sabathia suffered the injury. He continued to pitch into the eighth inning and appeared to be fine.
But Sabathia told the Yankees about the injury and an MRI revealed the extent of the strain. The injury requires six to eight weeks to heal.