The team said an MRI on Thursday showed no major structural damage after Davis hurt the knee going up for a dunk with 49 seconds left in Wednesday's victory over the Suns.
Davis predicted he will be out a week, and Celtics coach Doc Rivers echoed that assessment after practice Thursday.
"Nothing serious but he may be out for three, four or five days," Rivers said. "But it's nothing serious. He'll miss Friday (against Golden State). I think he'll miss a couple of games. But overall, that's pretty good."
Davis says the knee has been sore since he injured it in Game 7 of the NBA finals last year in Los Angeles.
"I've been playing with it all year," he said. "It's a sigh of relief, but you don't want to be hurt anyway. You don't want to sit out. You can't take that approach. It could be worse. I'm just glad I'm here [watching practice], getting healthy and getting ready to play."
Davis often has started at center in place of Shaquille O'Neal and Jermaine O'Neal, and entered last night having played all 59 games this season, tied for the team lead with Paul Pierce and Ray Allen.
Allen was given the day off Thursday after he came to practice and told Rivers and trainer Ed Lacerte that he had "soreness" in his legs. He is expected to be ready for the Warriors on Friday.
Rivers said O'Neal ran "skeleton" sets during practice, but has not been cleared yet to take part in full-contact practice.
Delonte West (sprained right ankle) isn't ready to practice, but was shooting around. Rivers said West will "definitely" miss Friday's game, as well as the Sunday's contest at Milwaukee.