"Thugs won't have the last word in Paris," Paris Mayor Bertrand Delanoe declared.
Fans threw stones and other objects at police, who replied by firing tear-gas canisters, and store and car windows near the Champs Elysees were smashed. Three police were among the injured.
"I would like to express my disgust and anger with regards to the surge of violence that several hundred thugs were responsible for," Delanoe said. "I ask the Interior Minister to step up the fight against this time type of phenomenon outside of the Parc des Princes stadium."
PSG players had been scheduled to show off the championship trophy from City Hall's balcony on Wednesday evening, but those plans were scrapped, the Paris mayor's office said.
Interior Minister Manuel Valls responded by summoning representatives from PSG, the French league, the police department, the mayor's office, and anti-hooliganism officials for a meeting.
"I obviously assume my part of responsibility in this fiasco," French league president Frederic Thiriez said in a statement, referring to the fact that the LFP had given the go-ahead for the presentation to be held at the Trocadero plaza, near the Eiffel Tower.
"The party was ruined and could have had dramatic consequences because of a bunch of thugs ... who have nothing to do with football but take advantage of it to take part in criminal activities," Thiriez added. "Paris didn't deserve this."
PSG's moonlit boat trip along the Seine river on Monday night also was cancelled.
PSG has not commented beyond a statement released late Monday night which said "today should have been a day of celebration for the city of Paris," but that "the party was spoiled by a few hundred troublemakers who have nothing to do with football."
A total of 800 officers were deployed to contain the supporters, and they took several hours to bring a situation under control.
Media reactions to the violence implicated former PSG fan groups in the violence.
But in a collective statement on Tuesday, these groups, known as ultras, said they were not involved in the violence and maintained they made pleas over loudspeakers in an attempt to calm the crowd.
Under former president Robin Leproux, PSG disbanded all known fan groups and radically changed ticketing policy following the death of a PSG supporter after fights outside Parc des Princes in February 2010. That followed the hooligan-related death of another PSG fan in November 2006 following skirmishes after a UEFA Cup match.