The twice All-Star, who last month signed a four-year contract extension worth $68 million with Boston, was forced to leave Tuesday's game against the New York Yankees after two outs in the fifth inning.
"It was a pitch to (Alex) Rodriguez that he flew out to left on," Beckett, 30, told the team's official website (http://boston.redsox.mlb.com). "My footing just slipped, and it just got tighter and tighter after that."
Veteran right-hander Joe Nelson, promoted from Triple-A Pawtucket, fills the opening in the team's 25-man roster.
(Writing by Mark Lamport-Stokes in Los Angeles; Editing by Ed Osmond)