Rookie Brandon Moss took Drew's sixth spot in the batting order and replaced him in right field.
Drew had been Boston's hottest hitter during its stay in Tokyo, belting two homers and driving in seven runs in the two exhibition games against Japanese professional teams.
It is unknown if Drew will be able to play the second game of this series on Wednesday. Following the two games against Oakland, the Red Sox will travel to Los Angeles and resume exhibition play with a three-game set against the Dodgers.
Boston's next regular-season games will be April 1-2 in Oakland.
Ian Browne is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.