NGOs working in the camp were taken by surprise on Monday morning when workmen, backed up by bulldozers, moved in to start dismantling shacks in the southern part of the camp.
In the afternoon some fires were started and stones thrown at police.
Later a group of about 150 migrants, some carrying iron bars, and activists gathered at the side of a bypass leading to the port, throwing stones at police and hitting vehicles on their way to the UK, where the camp's residents hope to go.
Local authorities say 3,700 people live in the camp and 800-1,000 will be affected by the eviction, although NGOs say the figure is much higher.
Evicted migrants have been offered heated accommodation in a limited number of refitted containers next door to the camp or in centres elswehere in France but many are reluctant to move there because they lack communal spaces and movement is restricted.
They are also concerned about being fingerprinted.
The European Commission said late Monday it will this week propose using funds usually earmarked for catastrophes outside the bloc to provide aid to EU countries affected by the migrant crisis.