Safonov made four straight penalty saves as PSG beat Brazil's Flamengo 2-1 in the shootout on Wednesday to secure the club's first global title. He was thrown in the air by his teammates during the celebrations.
PSG coach Luis Enrique said he thinks the injury was suffered during the shootout, before Safonov went on to secure PSG the trophy.
"I can't explain anything, it's incredible. The player doesn't know how it happened," Luis Enrique said in translated comments Friday.
"We think it was on the third penalty kick. He made a strange movement and fractured it. He saved the last two shots with the fracture. The adrenaline was so powerful that the player was able to do it without pain. It's incredible."
In a video posted on social media app Telegram, Safonov didn't address what happened directly, but said: "You know, no matter what happens, I can't be broken."
PSG said Friday that Safonov's "situation will be re-evaluated" after three or four weeks.
Safonov, PSG's Russian backup goalkeeper, hadn't played a single minute for the team until summer signing Lucas Chevalier sustained an ankle injury which has ruled him out since his last game Nov. 29.
Chevalier was on the bench against Flamengo. PSG's next game is a Coupe de France meeting Saturday with fifth-tier Vendee Fontenay.
Information from The Associated Press was used in this report.
