Ortiz was hurt while diving into first base attempting to beat out a double-play grounder in the final inning of Friday's 5-4, 11-inning loss to the Rays.
"I was hoping he wouldn't feel it today," Boston manager Terry Francona said before Boston's 2-1 loss. "We'll give him a little time and let it get better."
The injury is not considered serious.
Also, the Red Sox placed first baseman Sean Casey on the 15-day disabled list with a right hip flexor injury and recalled first baseman Brandon Moss from Triple-A Pawtucket. Casey was hurt while running the bases in Friday's game.
"He actually says he feels OK," Francona said of Casey. "The medical staff, they're not convinced that he can safely go out there the next couple days."
Right-hander Daisuke Matsuzaka, who missed his last start with flulike symptoms, threw a 50-pitch bullpen session at Fenway Park. Dice-K could make his next start Tuesday or Wednesday.