They have until 20:00 local time (19:00 GMT) on Tuesday to leave the southern part of the sprawling camp.
Anyone remaining will be forcibly removed to allow for the makeshift structures there to be  razed.
The area has become a cultural hub for many of the migrants. It has shops, a school and religious structures.
The authorities said up to 1,000 people could be affected but volunteers on the ground estimated that at least twice that number lived in the area.
Thousands of migrants from the Middle East and Africa have congregated around Calais in the hope of crossing to the UK.
Hundreds of migrants living in part of a camp in the French port of Calais known as the Jungle have been ordered to leave or face eviction.