Clermont's Parra in doubt for European Cup final
Parra suffered the "muscle injury" during last weekend's 27-22 European semifinal win over Irish side Leinster.
The 28-year-old "will be monitored in the days and weeks to come to determine the length of his absence", the club said.
Two-time European runners-up Clermont have already been hit by the absence of Noa Nakaitaci and Wesley Fofana for the Final against the English side in Edinburgh on May 13.
Also sidelined for Saturday's Top 14 clash against Lyon are centres Aurelien Rougerie (foot), Remi Lamerat (knee) and prop Davit Zirakashvili (ankle), who all took knocks against the Irish.
Agence France-Presse