The scrumhalf does not require surgery but is expected to miss up to three months after tests discovered he had suffered a fracture during his team's Champions Cup victory against Ospreys.
"The injury does not require surgery, but will lead to a six-week immobilisation before he can begin his rehabilitation. The duration of its unavailability is thus estimated between 10 and 12 weeks," Clermont said in a statement.
Stand-in skipper John Barclay is also a doubt for Scotland's games against Samoa, New Zealand and Australia next month as he battles to overcome a concussion problem.
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(Reporting by Tom Hayward, editing by Ed Osmond)
