Exeter Chiefs second row Peter Short has had an operation on the leg he broke in the 21-11 win over Wasps.
Short, 31, was stretchered off after 23 minutes of the match at Sandy Park.
"He'll obviously be out for a little while, how long that'll be is difficult to say at this stage," Baxter told BBC Radio Devon.
The former Leicester forward joined the Chiefs from Bath in June and had been an ever-present in the side in the Premiership this season.
"It's unfortunate for Peter, he's been playing really well for us but he'll still have a big part to play for us in the second half of the season," Baxter said.
"It's one of those things that happens in rugby but we're fortunate that we have some good players to step in.
"It's a pretty straightforward injury so we're relatively comfortable that he's going to be back full on and in good nick," he added.