Interior Minister Laurent Nunez said about 180 schools had been affected by the protests, mainly in the Creteil and Versailles districts around Paris, as well as in cities including Lille, Lyon, Grenoble and Nice, the DPA reported.
Nunez said preliminary figures showed 12 members of the security forces had been injured on Monday. Citing the education minister, he also reported that eight members of teaching staff, including three headteachers, and a dozen pupils had been injured.
"These were not demands; very often, it was simply violence in its purest form," Nunez said.
He added that police were investigating allegations of violence by officials.
Nunez said pupils had blockaded 27 schools on Monday and attempted to blockade another 50.
The protests began on Friday, with pupils protesting an array of grievances, including a lack of resources and teaching staff, overcrowded classrooms and heavy timetables.
The demonstrations are expected to continue on Tuesday, when a nationwide strike by public sector workers is also scheduled.