Eyewitnesses say workers have started to tear down unoccupied tents and shacks by hand.
Officials say demolition work has begun by hand to avoid inflaming tensions.
It is hoped the camp will be cleared by Friday.
The operation to clear it has been peaceful so far.
Police equipped with water cannon stood guard as hundreds of migrants – some of whom have lived in the squalid camp on the northern French coast for months or even years – waited for buses to take them to be resettled across France.
The Jungle in numbers
- More than 3,000 have been moved so far
- 1,900 left voluntarily on Monday
- At least 900 left on Tuesday
- 600 unaccompanied minors are being helped
- 1,200 police have been deployed
The end of a dream
Groups of young men who have fled war and poverty in the Middle East, Africa and Asia, keep warm around piles of burning rubbish.
A large fire blazed at one point but then appeared to be brought under control.
There was no repeat of the minor skirmishes with security forces seen over the weekend.
Officials say the operation was going peacefully.
For many of the migrants from Syria, Afghanistan and other conflict zones, the closure of the Jungle marked the end of a dream to reach the UK.
London and Paris
London and Paris have been at odds over the fate of around 1,300 unaccompanied child migrants living in the Jungle.
The French government last week urged the UK to step up its efforts to resettle them.
On Monday, British Interior Minister Amber Rudd said Britain would take in roughly half of the camp’s lone children.
Six months before a presidential election in France, the camp and border controls with Britain are hotly debated campaign issues.
Some right-wing opponents of President Francois Hollande want all the migrants sent to the UK.
The far-right National Front party said the current resettlement plan would create mini-Calais camps across France.
What they are saying
“The migrants have known for a long time this was going to happen. We are making sure it is done properly,” – Calais Regional Prefet Fabienne Bucco.
“We know the Jungle is over. We want a good city, like one near Paris. If we can’t go there, we will come back to the Jungle,” – Aarash, 21-year-old Afghan migrant.
“France is a good country but just not right for me and my situation. I am going to stay and I will build another jungle!” – Khan, a 32-year-old Afghan migrant.
“Overall, the migrants have understood that time is up for the Jungle. They have been receptive,” – social worker Serge Szarzynski.