The 33-year-old Australian lock suffered the injury at the end of the last campaign, but further tests showed that an operation was needed to correct the problem.
"It was felt a bit of rest and rehab would sort the problem out, but it became obvious, once we got back into the start of pre-season, that the issue hadn't really improved with a block of rest, so we investigated it a bit further," Exeter coach Rob Baxter told the club's official website.
"The fact we have managed to get on with things now, we are hopeful he won't miss too much of the season.
"He is probably unlikely to feature in the first game of the season, but we are hopeful he will be back fully fit relatively quickly and it will not be a half-a-season job."
Exeter get their Aviva Premiership campaign up and running away to London Welsh on September 7.