Drew, sidelined since August 18 because of a strained lower back, was hitting .280 with 19 homers and 64 RBIs before the injury.
After a disappointing regular season with Boston in 2007, Drew hit a grand slam in Game 6 of the ALCS, when Boston overcame a 3-1 deficit against Cleveland en route to its second World Series title in four years.
The Red Sox also recalled first baseman Chris Carter and catcher George Kottaras from Triple-A Pawtucket before Monday night's game against Tampa Bay.
Kottaras and Carter joined the Red Sox after Pawtucket was eliminated from the International League playoffs at Scranton-Wilkes Barre on Sunday.
Carter, acquired last August from Washington for outfielder Wily Mo Pena, was 2-for-3 in his major league debut in his only game with Boston on June 5.
Kottaras, picked up when Boston traded left-hander David Wells to San Diego two years ago, has never played in the majors. He hit .300 with 24 homers and 81 RBIs at Pawtucket.
In addition, the Red Sox assigned RHP Marcus McBeth to Pawtucket.