The arrests were made for “damage, violence or throwing projectiles,” Paris police said Monday, adding that more than 400 people were issued with a penalty for failing to wear a mask.
Images on social media show police in riot gear firing teargas to disperse PSG fans, while other videos show a car on fire and the team’s supporters throwing fireworks at police.
Fans also clashed with police outside PSG’s Parc des Princes stadium after the team’s 1-0 defeat.
PSG was appearing in its first Champions League final in Lisbon on Sunday, but Kingsley Coman’s second-half header means the French champion’s wait for European Cup silverware goes on.
Victory handed Bayern its sixth European Cup title and first since 2013.
On Sunday night, France’s Interior Minister Gérald Darmanin thanked police for arresting “violent groups” and “troublemakers” in Paris.
Meanwhile, deputy mayor of Paris Nicolas Nordman said the violence was “intolerable.”
He added: “The perpetrators have nothing to do with the love of football, with PSG, with Paris. They must be condemned. Thanks to the police and firefighters who intervened all night.”