Safonov saved four penalties in the shootout to hand the European champions the Intercontinental Cup title after a 1-1 draw with Flamengo in the final on Wednesday.
But PSG revealed the 26-year-old suffered a left-hand fracture and will be re-evaluated in three to four weeks, ensuring he will miss Saturday's French Cup game against Vendee Fontenay before the winter break.
"I can't explain it, it's unbelievable but the player doesn't know how it happened. We think it was on the third penalty kick that he made a strange movement. He has a fracture," Luis Enrique told reporters.
"With the adrenaline, he must have finished the (shootout) despite the fracture. It's incredible how all the players, including Safonov, have the ability to help the team, to always be ready to help the team. That's the mentality we want. You have to be ready to help the team and work all the time."
Luis Enrique said he had not spoken to Safonov yet, but that the injury was probably a sign he should rest.
"Everyone accepts and must also deal with the negative. It's karma, some would say. Negative things allow you to learn a lot," the Spanish coach added.
"He played a very great match in his last three or four outings. Life is telling him that he needs to rest and recover. With his mentality, he will come back faster than normal. He has a strong mentality."
Luis Enrique did not reveal whether Lucas Chevalier or Renato Marin will start in goal, saying: "I will inform the players first and then you will know my decision."
PSG also confirmed Lee Kang-In will be sidelined for several weeks after sustaining a left thigh injury against Flamengo, while Bradley Barcola is having treatment for muscle fatigue.
