Hawks chief executive Stuart Fox said Clarkson is mobile but won't be at work for another four weeks and it could be even longer before the two-time premiership coach is back at the helm.
"He's continuing to respond really well to treatment. We can confirm that doctors have advised us that he has a mild case of the condition and that the recovery still needs to be treated very seriously," Fox said.
"What we don't know is the length of the recovery.
"Alastair certainly won't be at work for the next four weeks. That could be a bit longer - we just don't know yet."
"He won't be at work for four weeks at an absolute minimum (and) we think that may be even longer."
Clarkson has made himself available to interim coach Brendon Bolton, although Fox reiterated that recovery was his focus.
"I suspect he'll have communication with the club as he did last week. I think it's going to help him, it's going to help us," Fox said.
"It's more a communication process rather than a decision-making process.
"Naturally, he's going to have some contact, but I think it will be more using his wisdom than anything else."
Clarkson is renowned for his high-paced lifestyle, but Fox said it hasn't been hard to hold him back.
"He's very determined but it hasn't been tough holding him back. I think he's well-aware that this has been a pretty serious condition," Fox said.
"He's treating it very seriously and I think for the first time I've been dealing with Alastair he's actually slowing down.
"Mentally I can't pick any change. His spirits are up, he's jovial, he's having fun."
Meanwhile, veteran Hawks midfielder Brad Sewell said Clarkson had instructed the playing group to keep their focus on winning games instead of his recovery.
"He's made sure that we all understand that we've got a job to do here and not to let that focus detract from what we need to be doing here at the moment," Sewell said.
"He knows that he's got all of our support and it's just a matter of time until we see him waltz back through the doors again."
The Hawks narrowly escaped a massive upset against last year's wooden-spoon winners on Sunday, but Sewell denied the coaching change had an impact on the reigning premiers' performance.
"Yesterday was a funny sort of scrappy game," he said.
"GWS were really good and it took us a little while to find our feet and deal with the conditions."
The second-placed Hawks host West Coast at Aurora Stadium in Launceston on Saturday.