France and the UK have traded accusations about the children's treatment.
Two large fires broke out on Friday morning at the camp, from which almost 6,000 people have been evacuated.
The evacuation is due to be completed on Friday and people refusing to leave would be arrested, Calais police said.
Migrants fleeing war and poverty had used the sprawling site as a staging post to try and reach the UK.
It had been seen as a key symbol of Europe's failure to deal with the worst migrant crisis since the second world war.
At least 1,500 minors have been staying at a special container camp at the site, but it has been full and many children have also reportedly been sleeping rough.
The British government said it had told the French authorities that they must "properly protect" children.
But French Interior Minister Bernard Cazeneuve said in a statement that the best way to protect the children was for the UK to "quickly execute its responsibilities to take in these minors".
The UK has agreed to take in nearly 250 of the children.
'We may never know where they've gone'
Save the Children said dozens of children have been exposed to "serious amounts of danger" during the clearance process. Some might have run away on their own, the charity warned.
"We may never know where they've gone," aid worker Dorothy Sang said.
The rest of those evacuated have been taken to reception centres around France, where they are being processed and will be able to apply for asylum.
But aid workers believe that hundreds, or perhaps even thousands of migrants might have fled the area before the clearance operation began on Monday.
Demolition work is continuing and the local authorities say the clearance will be completed by Monday.
Save the Children said dozens of children have been exposed to "serious amounts of danger" during the clearance process. Some might have run away on their own, the charity warned.
"We may never know where they've gone," aid worker Dorothy Sang said.
The rest of those evacuated have been taken to reception centres around France, where they are being processed and will be able to apply for asylum.
But aid workers believe that hundreds, or perhaps even thousands of migrants might have fled the area before the clearance operation began on Monday.
Demolition work is continuing and the local authorities say the clearance will be completed by Monday.
What is the Jungle?
The Jungle camp is near the port of Calais and close to the 31-mile (50km) Channel Tunnel
Officially about 7,000 migrants live in the camp. The Help Refugees agency said the final population ahead of its demolition was 8,143
The camp was halved in area earlier this year but the population continued to rise,and reports of violence have increased
Many migrants attempt to hide themselves in cargo vehicles entering the Channel Tunnel
The area has been hit by protests from both locals and truck operators