Vince, 25, suffered cartilage damage in his left knee when he twisted awkwardly to tackle Brisbane Lions premiership star Luke Power at the Gabba in round 20.
He sat out the last two games of the season, but recovered in time to start training with the team when the players returned for pre-season training on November 1.
Crows football operations manager Phil Harper said Vince had complained of more soreness in his knee after training last Thursday.
"Bernie pulled up a bit sore on Thursday," Harper told afl.com.au. "They [the doctor and surgeon] had a look at it and did an arthroscope, which showed there was a bit more cartilage there, so they took it out.
"He was running pain-free for the whole of pre-season until last Thursday, but with the timing of the break we thought it was a good idea for Bernie to have it [the surgery] now.
"It's a setback, but he'll be able to be running again when the players come back in January. He just won't join in full training again until mid-January."
Vince will join David Mackay and untried onballer Sam Shaw on modified programs when the players return to training in early January.
Mackay was booked in for surgery last month after his troublesome groin failed to respond to rest over the post-season break.
Shaw is being eased into training having missed much of last season with stress fractures in his back and shins.
Ruckman Ivan Maric (hip), promising forward Ricky Henderson (hip) and new recruit Richard Tambling (groin/knee) have also made slow starts after post-season surgery, but Crows physical performance manager Stephen Schwerdt said the injured trio would be ready to join in full training after Christmas.
"Sam and David are probably the only two players, who have been on significantly modified programs this pre-season," Schwerdt said. "They'll still be doing some training out on the track when the guys come back in January, but I wouldn't have thought they'd be training with the team just yet.
"Sam had a lot of trouble with stress fractures in his back, so we're just taking it really slowly with him to make sure he gets a lot of good strength in there before he charges into the stuff with the team."
The Crows made a raft of changes to their pre-season training program after enduring a nightmare run with injuries last summer.
Stars Jason Porplyzia, Chris Knights, Andy Otten and ruckman Brad Moran all fell victim to Adelaide's injury curse last pre-season, but Schwerdt said the important quartet had made a solid start this summer.
"None of those guys have missed a beat so far," Schwerdt said.
"They got a good block of training in and have a strong foundation to work off now. That was one of the main aims of this period, for the players to get a really solid foundation both with their running and their strength.
"Those guys have done that and have given themselves the best-possible preparation."
