Outfielder Ben Francisco was recalled from Triple-A Buffalo to take Westbrook's spot on the roster.
The Indians were already without closer Joe Borowski, who went on the DL last Tuesday with a triceps strain.
Westbrook, who missed almost two months last year with a left oblique strain, is 1-2 with a 2.73 ERA.
"Obviously, he's pitched very well this year," Cleveland manager Eric Wedge said. "This is why you work so hard to have depth. We talk about it year in and year out."
Wedge said Paul Byrd would move up to take Westbrook's scheduled start Friday against the New York Yankees. He said he would decide between left-handers Aaron Laffey and Jeremy Sowers to come up from Buffalo to take Westbrook's spot in the rotation.
"We've got a lot of confidence in some of our guys in Triple-A, particularly the starters," Wedge said. "We'll make a decision with that. I'm sure they'll come up here and do a good job for us."
Trainer Lonnie Soloff said Westbrook strained a left intercostal muscle while pitching on Saturday and would probably be out two to four weeks.
"The intercostal is a very small, thin muscle in between the ribs," Soloff said. "He's going to miss at least two starts and we will reassess his progress after the next five to seven days of conservative treatment."
Westbrook was given an MRI and put on oral medication to control inflammation.
"He was hoping to go down and in with a pitch and he hit a little extra and felt a tug," Soloff said. "He faced two hitters after that and his night was over."