Clerc picked up the injury in Toulouse's 19-14 victory over Biarritz in the French league on Friday.
"He will be out of action for eight to 10 days," the FFR said in a statement.
Clerc will miss his team's Six Nations opener in Rome in eight days but he could be back in the squad for the home game against defending champions Wales on Feb 9.
His replacement Bonneval, 22, has not won a single cap with France.
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