Beckett was hit on the left temple while shagging balls in the outfield during batting practice Monday.
Boston said Wednesday he has passed tests and been cleared for physical activity.
Right-hander Stolmy Pimentel will start in Beckett's place Thursday against the Philadelphia Phillies in Fort Myers. The Red Sox expect Beckett to take his turn after that, but the decision will be made after input from pitching coach Curt Young.
"He's allowed to do some activity," Red Sox manager Terry Francona said. "They'll monitory his activity. He'll do some biking and some light throwing, and see how he progresses from there. He's not going to pitch tomorrow. What well do is we'll keep him on his schedule to pitch his next time out. How he gets to that start is up to how he feels and how he and Curt decide to do it."