The organisation said it was concerned about the planned closure of the camp, known as the 'Jungle', saying it may lead to children disappearing before they can be processed.
Charities estimate there are around 400 unaccompanied children living there who are eligible to come to Britain.
Lily Caprani, the deputy executive director of Unicef UK, the UN body’s charitable arm in the country, told the BBC: "Last time part of the Jungle camp was demolished, hundreds of children went missing. We don't know what happened to them."
Despite this French President Francois Hollande vowed to have cleared the camp by the end of the year during a visit to the Jungle on Monday.
All of the camp’s estimated 10,000 residents will be forced to move to reception centres across the country.
Mr Hollande is under intense pressure to mitigate the rising tide of anti-refugee feeling and Islamophobia ahead of the French presidential election next year.
Far-right leader Marine Le Pen looks poised to at least make the run-off to become president and has vowed to stop France accepting anymore refugees.
The UK Government has also come under increasing pressure to take in the unaccompanied children.
On the first anniversary of the death of Aylan Kurdi, a three-year-old Syrian boy who was found dead on a Turkish beach, last month, migrant rights charity Citizens UK handed in a letter signed by several celebrities including Juliet Stevenson and Vanessa Redgrave calling on Home Secretary Amber Rudd to accept them.
Fewer than 20 children were granted asylum in the UK in the first three months of the year.
Lord Alfred Dubs, the peer who helped force the Government to accept an amendment to the Immigration Act which requires the UK to accept lone minors, said “deeply saddened” the Government was still “dragging its feet”.
Lord Dubs, who was himself a child refugee who came to the UK during the Kindertransport in 1939, said: “Now that the new Government has had some weeks to settle in after the EU referendum vote there really is no excuse for any further delay. Theresa May and Amber Rudd should be taking immediate action.”
Unicef is concerned that the children may fall into the hands of traffickers who may exploit them.
In September, The Independent revealed the Home Office does not know where 360 of the vulnerable children who have already arrived in the UK are. Of these, 81 have been missing for more than five years.
Over the past five years, 9,287 “unaccompanied minor” asylum seekers have been arrived in the UK.
A spokesman for the Home Office told The Independent the Government remained committed to resettling “vulnerable children” but said the closure of the camp was “a matter for the French government”.
He said: “The UK Government has made crystal clear its commitment to resettle vulnerable children under the Immigration Act and ensure those with links to the UK are brought here using the Dublin Regulation.
“We will also continue to support the French Government as it provides alternative accommodation to migrants in the camps and returns those not in need of protection to their home countries.”
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