"Unregistered minors are wandering around, lost, wondering where they will spend the night," said Samuel Hanryon, spokesman for Doctors Without Borders (MSF).
The warning came as the abandoned slum outside the port of Calais smouldered from countless fires set by departing migrants, causing many to flee without their possessions.
Riot police outside the camp's main entrance initially barred anyone from returning to the squalid settlement to retrieve their belongings, but later relented, allowing around 100 to go back in.
Top regional official Fabienne Buccio, announcing the end of the evacuation, said a "page has been turned" for the camp, which was a magnet for migrants hoping to sneak onto lorries or trains heading across the Channel to Britain.
But the fate of unaccompanied minors -- a source of deep concern and a bitter blame game between Paris and London -- was shrouded in uncertainty.
Some 1,500 are being housed temporarily in an on-site park of specially fitted shipping containers that is now full, according to the group France Terre d'Asile, responsible for their care.
"There is no more space in the container camp," said Pierre Henry, the group's director.
He told reporters that 40 children were due to be transferred to Britain on Thursday, adding to more than 200 that London took in last week. Another 40 have been sent to a temporary centre in eastern France awaiting news on their cases.
French Interior Minister Bernard Cazeneuve has said that all minors "with proven family links in Britain" would eventually be transferred there.
He added that London had committed to reviewing all other cases where it was "in the child's interest" to settle across the Channel.
Success in closing down the camp and resettling its residents carries heavy political implications for President Francois Hollande, who is deeply unpopular and has yet to decide whether to seek re-election next year.
'We left our nations in flames'
Most of the migrants hoping to reach Britain had fled conflict or persecution in countries such as Eritrea, Sudan and Afghanistan.
"We left our nations behind us in flames, only to find the Jungle go up in flames too," said Aziz Yaacoub, a 25-year-old from the troubled Sudanese region of Darfur.
The authorities have said those who agree to be moved can seek asylum in France.
Buccio said "at least 6,600" would have left the camp by the end of Wednesday, most boarding buses to shelters around France.
Estimates of the camp's population ranged between 6,400 and 8,100 before the operation began Monday.
Demolition crews continued Wednesday to tear down the Jungle's tents and makeshift shelters.
Their work was impeded -- and paradoxically speeded up -- by the fires that ravaged many of the ramshackle dwellings.
Firefighters, volunteers and migrants joined forces against the blazes, but the going was tough in the smouldering maze of alleyways.
Migrants and officials alike said the fires were set deliberately, while gas cylinders previously used for cooking had exploded and caused the blazes to spread.
Police said four migrants had been arrested on suspicion of arson.
Many locals fear new settlements will simply spring up in the area once the Jungle is razed.
Calais Mayor Natacha Bouchart said the announcement of the end of the camp was premature, pointing to the remaining unaccompanied minors and perhaps hundreds of former residents who have slipped out into the surrounding area.