Vince, who had an injury-interrupted pre-season, struggled to recapture his best-and-fairest winning form of 2009 in the opening month of the season, and was dropped after the loss to Carlton in round five.
He starred for SANFL club Woodville-West Torrens last weekend and was on the verge of a recall when he strained his hamstring on Thursday morning.
Crows assistant coach Ben Hart said the club was yet to put a time frame on Vince's return.
"It's disappointing for Bernie. What we asked him to do when he went back to the SANFL he did really well on the weekend," Hart said on Thursday.
"He worked on his running game … and was in line for a recall, so it's disappointing for him. Hopefully, it's not a bad one [strain]."
In-form onballer Scott Thompson (corked calf) stayed indoors on Thursday and will need to prove his fitness at training on Friday morning.
Patrick Dangerfield, who was concussed in the much-publicised tackle from Melbourne midfielder Jack Trengove, had a light run and will also attempt to increase his training load at the last session of the week.
Hart was confident both players would be available to play against the Suns.
"I think they [Thompson and Dangerfield] are better than 50-50," he said.
"They're improving every day and we're going to give them as long as we can, but they'll need to do something tomorrow.
Promoted rookie Matt Wright shrugged off a knee sprain to complete training and has been included in the team to take on the Suns.
Utilities James Sellar and Jack Gunston have been named to play their first matches of the season, while Richard Tambling has been recalled after a one-week suspension for striking.
Leading goalkicker Taylor Walker has been dropped alongside Brad Symes and unlucky defender Jared Petrenko.
Hart said a number of players had put themselves at risk of being dropped after the big loss to Melbourne last weekend, adding that only four players, Kurt Tippett, Matthew Jaensch, Rory Sloane and Chris Schmidt, had received pass-marks in the 96-point defeat.
"We spoke to a lot of guys about their form on the weekend and to be quite honest we spoke to a lot of them about the possibility of missing out," he said.
"There were maybe three or four guys last week who tried their best to stay at the standard with the intensity and the way they played the game.
"It's fair to say if you keep dishing up that you won't be in the side too long."
The Crows are being hamstrung at selection by a mounting injury list, which features names like Vince, Jason Porplyzia (shoulder), Phil Davis (shoulder), Mackay (AC joint), Scott Stevens (ill) and Andy Otten (knee).
Otten will attempt to run on his troublesome knee on Saturday, while Stevens is expected to return to training next week.
Hart admitted the club's depth was being tested by the spate of injuries.
"We've got enough people there, but it's also about the way you make up your side and who goes into different spots. There are still a few avenues for us, but we wouldn't want to get too many more injuries," he said.
"You can be temped to [make changes] but one, you've got to have people to be able to bring in and two, you'd also like to see the group respond after they performance they've given."
Katrina Gill covers Adelaide news for afl.com.au. Follow her on Twitter: @AFL_KatrinaGill
