The 20-year-old forward from Saratov injured his left ankle and also strained ligaments in his wrist when he tried to break his fall.
He had to be helped off the court in the 76-69 French win.
Doctors for Russia’s national team and CSKA say that Monia’s injuries are not serious, but he will wear a cast on his arm while he recovers.
The 6ft 6in star’s brightest moment in Sweden came in the elimination round game against Croatia, when he came up with a late steal and dunk to put Russia in front for good at the end of the game.
He averaged more than eight points and almost five rebounds a game.