The Frenchman, who joined Atletico from AS Monaco in 2018, had left the pitch on a stretcher.
"Following tests carried out on the French player, the medical report from the club's medical services indicates that he has a ruptured right Achilles tendon and will have to undergo surgery," Atletico said in a statement on Sunday.
"All the best Thom, we wish you a speedy recovery."
Diego Simeone's side, who are seventh in LaLiga with seven points in four matches, play their Champions League opener at Lazio on Tuesday before hosting Real Madrid in the league on September 24.