As many as 50 police officers were sent to the scene, with firefighters present at the camps extinguishing fires.
Le Parisien reported that more than 20 were injured and 14 were hospitalized after the fight.
Only a week ago, on May 25, media reports suggested there was a fight at a migrant center in Calais involving 200 people that left 14 wounded.
The Calais new jungle camps are situated not far from the new Jules Ferry camp, the first institution in the city to provide shelter for migrants since the closure of the Sangatte refugee camp in 2002.
In recent months, French authorities have been shutting down illegal migration camps in Calais.
In April, a Pas-de-Calais Prefecture spokesman told Sputnik that there were some 1,900 undocumented migrants from Eritrea, Albania, Afghanistan, Sudan, Egypt and Syria living in various camps in Calais.
