Stevens copped a knock to his head at training following the Crows' loss to Fremantle in round three.
The 29-year-old passed a concussion test, but developed migraines and nausea the next day.
He felt well enough to complete the club's main training session last Thursday, but ruled himself out of the game against Port Adelaide when his condition deteriorated.
Stevens completed the warm-up at training on Tuesday before leaving the track as planned and completed a session on Wednesday, but made himself unavailable a short time later after becoming ill again.
He has a history of concussions and often takes several weeks to recover from a serious bout.
Football operations manager Phil Harper said it was impossible to put a time-frame on Stevens' return.
"It will continue to be a week-by-week situation with Scott," Harper said.
"We are not sure when he'll be able to return to full training, but he will continue to work through the symptoms with the medical staff."
Stevens has reported four concussions in the past two years.
The former Sydney Swans forward missed three games after being concussed against Fremantle in round one last season and sat out Adelaide's clash with Geelong in round four of 2009 for the same reason.He also missed the club's NAB Challenge game against Freo at Thebarton Oval in March this year after receiving another knock at training.
Stevens' slow recovery from the latest concussion sparked speculation he could be forced to retire on medical grounds, but Harper denied that was the case.
"We sent Scott off to the specialist who he's been to before, and he did a whole series of tests on Scott," Harper said. "The specialist suggests it [the concussion] isn't having long-term effects and that's why the tests were done. Scott's no worse off today than he was a couple of years ago when he got a big knock. "Is it a concern? Yes, any head knock to Scott Stevens will always be a concern for us, but the specialist is saying there's nothing to be alarmed about."
There was some good news for the Crows on Wednesday, with midfielder Patrick Dangerfield (illness) and defender Luke Thompson (ankle) both completing training.
Experienced players Michael Doughty and Richard Tambling should also be fit to take on the Blues after impressing at training on Tuesday.
