The five, aged between 18 and 48, were arrested on Wednesday and admitted using iron bars and pickaxe handles to attack three Syrian migrants near Calais station on the night of 20 January, police sources told the AFP news agency.
They are also said to have confessed to attacking a 13-year-old migrant an hour earlier.
Although they have not admitted dressing up as police officers, they are said to have "clearly tried to lay the blame for their actions on the police" by shouting "Police!" when they approached the migrants, dressing in clothes of the same colour as police uniforms and using walkie-talkies and truncheons.
They are also alleged to have stolen the Syrians' mobile phones and other property.
They deny stealing money but one of the victims says he was robbed of 4,000 euros.
Police believe they could have attacked several dozen people.
One of the suspects told police he was a member of a group that has organised protests against the "Jungle" migrants' camp in Calais and explained the attacks by their feeling that they had "had enough" of the shanty town, which housed some 4,000 people before the authorities cleared half of it at the beginning of the month.
These are not the first arrests for assaults on migrants in the area.
On 22 February three men and a woman were arrested in Lille after several months' inquiry into attacks.
On 11 February seven men were caught in the act of assaulting five Iraqi Kurds at Loon-plage, near Dunkirk, and remanded in custody.