Hospital staff tried to prevent the group from entering the hospital, and then from accessing an emergency room, telling them "there are patients in here."
The director of the hospital was present at the time and she said that in the group there were some wearing yellow reflector-vests, some not, and some had their faces covered.
Police said they had arrested 30 people.
Public hospital service chief Martin Hirsch said " I don't know what is the reason for this inexplicable intrusion. I don't know whether they were invading the hospital of fleeing something." He added that they would lodge a formal complaint.
The Pitié-Salpetrière Hospital is near the Place d'Italie on the Left Bank, which is where the trade union march ended amid clouds of tear gas.
The French interior minister, Christophe Castaner, suggested the incident was an "attack" carried out by dozens of far-left, anti-capitalist militants belonging to the so-called black blocs.
French Prime Minister Edouard Philippe denounced on Thursday the “totally irresponsible” intrusion into the hospital of La Pitié-Salpêtrière, questioning the “justification for these challenges” of a public service.
The fact of “entering a hospital while you are demonstrating (is) stupid, and basically scandalous. To disrupt the functioning of a public hospital service in this way is totally irresponsible,” Philippe said.
The big rallies in were largely peaceful in most cities. Paris was the scene of most clashes between police and marchers.