Beckett was removed in the third inning of Tuesday's game against the Detroit Tigers after suffering back spasms while pitching on a wet mound at Fenway Park.
Beckett also is questionable to throw a bullpen session Friday, and the Red Sox have not determined whether he will need a trip to the disabled list.
"He's not throwing today and I'd say it's questionable for him to throw tomorrow, which would then make it questionable that he would make his next start, which means he won't make it, more than likely," Valentine said Thursday.
"He feels much improved today and had a great night's sleep. He's still a little limited in his motion."
Red Sox pitcher Franklin Morales will be available out of the bullpen Thursday against the Minnesota Twins. But Valentine indicated Wednesday afternoon that Morales would be the one "waiting in the wings" if Beckett can't start Sunday against the Twins.
"I'm going to talk to Josh and see what he (thinks)," Valentine said. "He's been through this a couple of times before and I'll just get all the information and figure out if Tuesday's feasible or Wednesday's feasible, and what that does to the rest of the staff and if it would be better to give him the entire break."
This is the third time since 2010 that Beckett injured his back while pitching on a wet mound.