Far-right groups and pro-migrant activists have turned the mountain passes by the border, which are used by migrants travelling from Italy to France, into a stage for "provocations" and "posturing", Gerard Collomb said.
"Faced with these unacceptable actions," the minister, whose controversial immigration law was adopted Sunday by the National Assembly, said "significant police and gendarme reinforcements" would be deployed.
The extra security forces will "ensure absolute respect for the control of the border," he added.
Late Saturday and early Sunday, activists from a small French far-right group blocked a key mountain pass some six kilometres from the Italian border which they say is a "strategic point for illegal migrants", prompting a furious reaction from pro-migrant activists.
French gendarmes standing guard as demonstrators take part in a protest walk to help nearly 30 migrants to cross the border to France. Photo: AFP
On Sunday afternoon, a procession of French and Italian pro-migrant groups crossed the border at the Montgenevre Pass, alongside some 30 migrants, and had some minor scuffles with law enforcement officials on the way, a police source said.
The interior ministry said "violence was committed against security forces and a gendarme vehicle was damaged".
Thousands of young men from francophone west Africa have trudged across the mountains over the past two years, dreaming of jobs in France.
In recent months, as news about the route -- one of the lesser known on Europe's migrant trail -- filtered back to Africa, the arrivals have gained pace.
Most of those crossing the Alps in recent months have been from Guinea or Ivory Coast, both former French colonies.
French gendarmes clashing with demonstrators. Photo: AFP
Few have any hope of being granted refugee status, being considered economic migrants for fleeing a crippling lack of jobs and opportunities at home rather than war.
Collomb said the legislation passed Sunday aims for "better controlled" immigration, halving the waiting time for asylum applications to six months while also making it easier to deport those turned down as "economic" migrants.
However the legislation, criticised by rightwingers for being too soft and by leftwingers who see it as repressive, has exposed unprecedented divisions in President Emmanuel Macron's young centrist party.