The 25-year-old was one of three Hawks casualties on the night, with Paul Puopolo a late withdrawal after experiencing tightness in his quad during the warm-up, and Josh Gibson hurting his left ankle late in the game.
Birchall suffered his injury early in the match, but played on until midway through the third quarter, when he was replaced by late inclusion Xavier Ellis.
The rebounding defender failed to have his usual influence, managing only nine disposals, but Clarkson praised his courage in battling on once hurt.
"It affected him a fair bit," Clarkson said.
"He just hung in there for us until late in the third quarter; we didn't want to sub him too early.
"He battled manfully under a fair bit of duress.
"I think he'll be OK to play next week, but he'll need to recover pretty well and get himself right."
Clarkson was unsure of the seriousness of Gibson's injury.
The key defender appeared in serious pain when he rolled his ankle on the intersection of the natural and artificial turf along the Etihad Stadium boundary line.
"I haven't spoken to the docs to get an assessment on that one," Clarkson said.
The Hawks have a nine-day break before taking on the Brisbane Lions in Launceston next Sunday, giving the trio extra time to recover.
