England's Underhill, 28, was yellow carded after making contact with Lyon full-back Davit Niniashvili's head in a challenge during Friday's 37-12 in Cardiff.
English Premiership leaders Bath's next game is at Saracens on Saturday. They have already secured a home play-off on June 6th, with the final scheduled for a week later.
"The date when Underhill can return to play will be determined once his future playing schedule is confirmed," EPCR said.