PSG's Skriniar needs ankle operation after injury in Champions Trophy final
The Slovakia international, who has made 16 league appearances for PSG this season, was unable to continue after hurting his left ankle during an attempted clearance in the 70th minute.
"Unfortunately, after the match against Toulouse, the doctors ran tests on Milan and determined that he needed an operation," Enrique told reporters.
"Until this takes place and we see how it goes, we won't know how long he will be out for... it's a bad piece of news.
"(Injuries) are part of high-level sports. We cannot prevent that, it's part of a professional footballer's life."
PSG begin their French Cup campaign against regional league side Revel on Sunday, and Enrique insisted the two-time defending top-flight champions will be cautious about the threat their opponents pose.
"They are not a professional team, they compete in an amateur league. They are top of their league," Enrique said.
"There is therefore a significant difference, but that doesn't mean they won't pose a threat. If we don't prepare for the match adequately, it could turn into a bad evening... we're treating this match as if it were a league encounter."
Five points ahead at the top of the league, PSG resume their title defence on January 14th at Lens.