Thauvin was carried from the field on a stretcher during Thursday's 3-1 Europa League victory, prompting fears the winger has suffered a serious injury.
The 25-year-old has been one of the stars of Marseille's season, scoring 16 Ligue 1 goals and providing 13 assists for his side.
Such form has seen the former Newcastle wideman force his way into France manager Didier Deschamps' plans for the World Cup despite possessing almost unrivalled riches when it comes to forward players.
And Garcia remains hopeful that Thauvin could even be back in action for the return leg in Bilbao next week.
"Thauvin received a big bruise, but nothing is broken," Garcia told a press conference.
"We'll wait till tomorrow for more information."
Marseille currently sit third in the Ligue 1 table as they chase a return to the Champions League for the first time since 2013-14.