"He's day to day, and we'll hope he's back to us in a short period of time," Red Sox manager John Farrell said.
Betts is Boston's best all-around player, so his health is of vital importance as the club gets closer to October.
"He takes comfort in knowing that he's got some inflammation that we're dealing with but not to the point where structurally anything's going on there," Farrell said. "I think what he's also showed [previously] was the ability to get back in the lineup quick, and I would think that that could be a similar situation with this."
As the Red Sox try to finish their goal of winning the American League East, which could happen as early as Wednesday, they are being forced to do so with an undermanned lineup.
Second baseman Dustin Pedroia (swelling in left knee) and utility man Eduardo Nunez (right knee injury) were also out of the lineup, and it's uncertain when they will return to action.
Pedroia has served two stints on the disabled list due to a left knee that has bothered him all season.
"Pedey's still dealing with a little bit of swelling, and our approach with him has been to just get him as [healthy] as we can throughout the remaining games to have him as, like I said, most fresh and capable once we get to the next stage," Farrell said.
Will Pedroia's knee be sturdy enough to allow him to start regularly in the postseason?
"I'm confident that he will because he's going to do whatever is needed or certainly whatever it takes," Farrell said. "But in the interim, he's working to get a little of the swelling out of there today."
Nunez sustained a sprain in the PCL of his right knee on Sept. 9, and his return to the lineup on Monday was short-lived when he aggravated the knee on a swing in his second at-bat.
Will Nunez be able to play again before the regular season ends on Sunday?
"Certainly hopeful," Farrell said. "That would mean he's feeling better in a relatively short period of time. But he came in today, he was walking around without any evidence to it in just walking, but we know as the intensity climbs, that'll be the biggest test."