Police fired tear gas around midday, about 150-200 migrants and activists threw stones, and three makeshift shelters were set ablaze, according to a Reuters photographer at the site.
Earlier, one person was arrested for trying to stop a group of about 20 workers under heavy police protection from clearing the site, where about 3,000 people are staying.
"The migrants are just going to run and hide in the woods and the police are going to have to go after them," said activist Francois Guennoc of the Auberge des Migrants migrant support group.
Regional Prefect Fabienne Buccio had said the police presence was needed because "extremists" could try to intimidate migrants into turning down housing offers or buses to reception centers.
Interior Minister Bernard Cazeneuve said last week that authorities would work with humanitarian organizations to relocate the migrants to a nearby park of converted shipping containers or other reception centers around France.
On Thursday, a judge upheld a government order to evict migrants living in the southern part of the camp, although a few makeshift buildings of social importance such as a school and a theater are to remain untouched.
Thousands of migrants fleeing war and poverty, from Afghanistan to Syria, have converged on the northern port over the past year.
Many attempt to climb illegally onto trains using the Channel Tunnel or into lorries heading to Britain where they hope to settle. Their presence has led to tension with some of the local population and to a permanent police deployment.
Earlier on Monday at another European migrant crisis flashpoint, Macedonian police also fired tear gas to disperse hundreds who stormed the border from Greece. The migrants had torn down a gate as frustrations boiled over at restrictions imposed on people moving through the Balkans.