One volunteer, from La Vie Active charity, was shot in the face, and one of the policemen in the chest, local police have confirmed.
At least ten have been taken to hospital.
Some 200 migrants were involved in the fight, which started as the Jules Ferry charity was giving out meals. It then spread to other parts of the camp.
250 homes, 20 kitchens, and the Medicins sans Frontieres tent were damaged in fires, leaving over 500 people without shelter and food.
A burning smell and a black cloud of smoke was noticeable in the centre of Calais, several miles away.
250 police and 70 fire fighters attended the scene, which was under control by 20:00, the prefect of Pas-de-Calais, Fabienne Buccio, said.
In a press conference at the camp, she said situations like this had happened before, but never on such scale.
An eyewitness told local media she heard explosions, "like the sounds of gunshots, or tear gas being fired," and migrants carrying rocks, iron bars, and knives.
Prosecutors opened an inquest into the violence today.
Medicins sans Frontieres said today that an estimated 5,000 refugees are still living in the Jungle, despite the forced eviction by French Authorities of nearly half of the refugee camp in March.