Dembele's teenage teammate Desire Doue was named Champions League young player of the season by European football governing body.
Dembele struggled early in the campaign, dropped by coach Luis Enrique for a league phase game with Arsenal for disciplinary reasons, but the 28-year-old went on to score eight Champions League goals after his switch to a more central role.
While Dembele failed to find the net in PSG's 5-0 thrashing of Inter Milan in Saturday's final in Munich, he was singled out by the manager for his performance.
"I would give the Ballon d'Or to Mr. Ousmane Dembele," Luis Enrique said. "The way he defended tonight, just that alone could be worth the Ballon d'Or. That's how you lead a team. Goals, trophies, leadership, defence, his pressing."
The 19-year-old Doue wrapped up his extremely impressive campaign by creating the opening goal in the final for Achraf Hakimi before scoring twice himself.
PSG had seven players named in the competition's team of the season while humbled finalists Inter had just one included.
Team of the season
Goalkeeper: Gianluigi Donnarumma (PSG)
Defenders: Achraf Hakimi (PSG), Marquinhos (PSG), Alessandro Bastoni (Inter), Nuno Mendes (PSG)
Midfielders: Vitinha (PSG), Declan Rice (Arsenal)
Forwards: Lamine Yamal (Barcelona), Desire Doue (PSG), Ousmane Dembele (PSG), Raphinha (Barcelona)