The Red Sox hope Beckett won't miss more than a start or two, but will have a better idea of his status in the next few days, a team source told ESPNBoston.com's Gordon Edes.
Beckett left in the fourth inning of Monday's start at Toronto after experiencing pain in his ankle on consecutive pitches. He flew back to Boston on Tuesday to be examined by a specialist.
After seeing foot and ankle specialist Dr. George Theodore at Massachusetts General Hospital, Beckett was diagnosed with a simple sprain. No structural damage was found.
In a statement, team medical director Dr. Tom Gill said Beckett's exam results were "consistent with an ankle sprain." He will be re-evaluated later this week.
Asked to comment on the severity of Beckett's sprain, Red Sox manager Terry Francona declined to get into specifics.
"You saw the statement," he said. "Why don't we just stick to the statement?"
A team source told ESPNBoston.com on Wednesday morning that it would "take a few days" to determine the severity of the sprain.
Following Sunday's 11-inning loss, Beckett told reporters he had no idea how his ankle would feel the following morning.
"I could wake up tomorrow and feel like playing basketball," he said.
Instead, he flew back to Boston alone for tests.
Francona wasn't sure whether Beckett would rejoin the team in Toronto or wait until the Red Sox head south to Florida on Friday.
"I told him to wake up tomorrow and see how he's feeling and we'll go from there," Francona said following Tuesday's 14-0 rout of the Blue Jays.
He added: "I don't know that we really need to speculate. Let's let this thing settle down, let the medical staff work, and we'll get him back whenever he's supposed to be."
Informed of Beckett's diagnosis after pitching seven shutout innings to beat the Blue Jays Tuesday night, Lester was happy to hear the good news.
"(Encouraged) is kind of an understatement," Lester said. "It's big that it's just a sprain. Hopefully he'll be back in a couple of days rather than a couple of weeks. That's good news to hear."
Catcher Jarrod Saltalamacchia was equally enthusiastic.
"We need him, we need him for the long haul," Saltalamacchia said. "(Losing Beckett) would be a big hit for us."
An All-Star for the third time this season, Beckett is 12-5 in 27 starts. His 2.49 ERA is tied with Los Angeles Angels right-hander Jered Weaver for second lowest in the AL, behind Detroit's Justin Verlander (2.34).
Second in the AL East, the Red Sox are already dealing with injuries to key players. Right-hander Clay Buchholz has been out since June with a stress fracture in his back and is throwing from flat ground. Outfielder J.D. Drew is battling a sore left shoulder and finger injury.
Information from ESPNBoston.com contributor Ian Harrison and The Associated Press was used in this report.