The local state authority, the préfecture, in the Channel port has issued a decree ordering the southern part of the camp to be cleared of people and their possessions by 8.00pm on Tuesday.
"After this deadline, if they have not left the area, the evacuation of the occupants of this area will take place, if necessary by force," it announced.
Tents and improvised shops, cafés, churches and mosques will be razed in an effort to clear the area near a motorway leading to the port, where migrants have clashed with police on several occasions.
Some 3,700 people - many of them refugees from Syria and Iraq - live in the Jungle and the préfecture says that 800-1,000 live in the area in question.
NGOs working in the area say the figure is nearer to 2,000.
Officials say that tension with the local population has risen over the last three weeks, with police and residents' vehicles being stoned, and claim that some migrants are being manipulated by ultra-left "extremist movements".
They also note attacks on migrants by members of far-right "radicalised groups".
A rally to be held on Saturday in support of Piquemal was banned but self-styled "ex-servicemen" called on sympathisers to join a "citizens' walk" around the town on Saturday.
The right-wing mayor of Calais, Natacha Bouchart, has been demanding the closure of the whole of the Jungle for several weeks.
Although officials say the migrants will be housed in converted containers, where 300 places remain free, or moved to 98 centres elsewhere in France, NGOs say the proposed accomodation is not adequate.
On Thursday eight of them appealed to Interior Minister Bernard Cazeneuve to hold off on eviction.