Crawford, who signed a seven-year, $142 million contract with the Red Sox before the 2011 season, has already missed most of the current campaign following off-season wrist surgery.
He made his first appearance July 16, hitting .282 with 10 doubles, three homers, 19 RBI and five stolen bases in31 games.
"Carl Crawford has a chronic left elbow ulnar collateral ligament tear," a team statement said. "While he has been following a conservative treatment protocol and playing with this injury, his symptoms are getting worse."
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