The fight broke out as food was being distributed at the Jules-Ferry aid centre, local officials said.
It spread to a neighbouring container camp set up by local authorities, police added.
An AFP reporter at the scene also reported that several makeshift shelters within the main camp had been burned down.
The situation had calmed down by early evening.
Fights have frequently broken out in the tense and desperate atmosphere of the camp, which is roughly divided between the main communities -- primarily Afghans, Sudanese, Kurdish and Syrian.
Thousands of migrants and refugees have camped out there, hoping to smuggle themselves aboard lorries that are crossing the Channel to Britain.