The Calais Migrant Solidarity group released the amateur video on its website, showing policemen forcefully removing migrants from trucks, spraying them with tear gas and throwing them over a motorway barrier.
The group says the footage dates back to 5 May, a day after French Interior Minister Bernard Cazeneuve visited Calais.
"The exact circumstances of this intervention will be rapidly examined … and any failure to apply the ethical rules will be punished," the police said in a statement on Tuesday.
Prosecutor Jean-Pierre Valensi of Boulogne-sur-Mer near Calais told AFP that he had summoned the police's internal inspection body over the video.
The investigation comes months after Human Rights Watch condemned police abuse of migrants in Calais, a major departure point for migrants without papers attempting to reach the UK by rail or sea.
The group has also criticised the slow response of the French government in addressing poor living conditions.
Many migrants from Sudan, Syria, Eritrea, and Ethiopia live in makeshift camps in Calais, while Britain has demanded more action by French authorities to stem an increase in the numbers attempting the crossing.
Police at Pas-de-Calais said more than 300 migrants arrived on Tuesday on roads leading to the Channel tunnel.
During Cazeneuve’s visit earlier in the month, the country’s interior minister encouraged migrants to claim asylum in France instead of going to the UK.
“Too many migrants who could benefit from asylum in France are still hesitating” in the hope of reaching Britain, he said. “Asylum in France is the best opportunity for them.“