Weeks, manager Bob Melvin said, is day to day and close to returning to game action.
The young second baseman was enjoying a productive spring before the injury, collecting hits in six of his first 11 at-bats -- including a home run -- for a .545 average, to go along with five RBIs in just four games.
Sizemore, meanwhile, could return to the lineup as soon as Thursday after being hit by a pitch in the left hand on Sunday. He took grounders on Monday and hit in the cage Tuesday morning, both signs of progression.
The two infielders are the top candidates to open the regular season as the starting second baseman.
Jane Lee is a reporter for MLB.com. Read her blog, Major Lee-ague, and follow her on Twitter @JaneMLB. This story was not subject to the approval of Major League Baseball or its clubs.