Bernard Boucault, the Paris police commissioner, confirmed to several media outlets that 30 people had been injured as a result of the unrest, including three members of the security forces.
He also added that 21 people had been arrested for throwing projectiles and causing damage as fans and riot police clashed on Place du Trocadero, which is near the Eiffel Tower.
And in a statement published on their official website on Monday evening, PSG said: "Today should have been a day of celebration for the city of Paris, for the club, our fans and partners.
"The party was spoiled by a few hundred troublemakers who have nothing to do with football and even less with those that fill the Parc des Princes on match days with such passion and enthusiasm and in total security.
"All the members of the club, the players and the directors, express to all those loyal and passionate fans their heartfelt regret that today's trophy presentation ceremony had to be cut short.
"The celebrations will continue this Saturday at the Parc des Princes for the Ligue 1 match against Brest, when the club and its fans will unite in the joy of Paris Saint-Germain's first league title in 19 years.
"Paris Saint-Germain is more determined than ever to build a huge European club, worthy of the French capital, and far removed from those intent on trying to destroy that dream."
Carlo Ancelotti's men sealed their first domestic league crown since 1994 with a 1-0 win at Lyon over the weekend.