Beckett's next start was moved from Saturday to Tuesday after he developed a sore right elbow that created numbness in his hand.
Francona described the soreness as a "crick" in the pitcher's elbow that developed when he slept on it overnight.
"You wake up and have some inflammation. That's basically what it is," Francona said Wednesday. "Not an aneurysm or a clot."
Beckett was originally scheduled to pitch Saturday against Toronto. Instead, he's tentatively set to start Tuesday night when the Red Sox play New York at Yankee Stadium. But Francona said if that day comes and Beckett's elbow is still sore, he could be moved back again.
"If he's not ready, we won't pitch him. We'll back him up another couple days," Francona said. "That's the way it goes. I don't think that is going to happen, but if it did, we would back him up and I told him that.
"We'll pitch him when he's ready to pitch and not because his day comes up."
Beckett probably won't throw on the side until Friday, though Francona said the right-hander was "begging" to pitch now.
"The point is that Beckett is really wanting to throw, and that's always a good sign," Francona said.
In other injury news, outfielder J.D. Drew was held out of the starting lineup for a third straight game Wednesday with a stiff back. But Francona expected him to play in the weekend series against the Blue Jays.
Also, knuckleballer Tim Wakefield (shoulder tightness) threw on the side Tuesday and was scheduled for another session Wednesday.
"I would not rule him out for New York," Francona said, referring to an Aug. 26-28 series, "but the one thing we don't want to do is rush him back."