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.
Refugee crisis - in pictures
Refugee crisis - in pictures
A child looks through the fence at the Moria detention camp for migrants and refugees at the island of Lesbos on May 24, 2016.
Ahmad Zarour, 32, from Syria, reacts after his rescue by MOAS (Migrant Offshore Aid Station) while attempting to reach the Greek island of Agathonisi, Dodecanese, southeastern Agean Sea
Syrian migrants holding life vests gather onto a pebble beach in the Yesil liman district of Canakkale, northwestern Turkey, after being stopped by Turkish police in their attempt to reach the Greek island of Lesbos on 29 January 2016.
Refugees flash the 'V for victory' sign during a demonstration as they block the Greek-Macedonian border
Migrants have been braving sub zero temperatures as they cross the border from Macedonia into Serbia.
A sinking boat is seen behind a Turkish gendarme off the coast of Canakkale's Bademli district on January 30, 2016. At least 33 migrants drowned on January 30 when their boat sank in the Aegean Sea while trying to cross from Turkey to Greece.
A general view of a shelter for migrants inside a hangar of the former Tempelhof airport in Berlin, Germany
Refugees protest behind a fence against restrictions limiting passage at the Greek-Macedonian border, near Gevgelija. Since last week, Macedonia has restricted passage to northern Europe to only Syrians, Iraqis and Afghans who are considered war refugees. All other nationalities are deemed economic migrants and told to turn back. Macedonia has finished building a fence on its frontier with Greece becoming the latest country in Europe to build a border barrier aimed at checking the flow of refugees
A father and his child wait after being caught by Turkish gendarme on 27 January 2016 at Canakkale's Kucukkuyu district
Migrants make hand signals as they arrive into the southern Spanish port of Malaga on 27 January, 2016 after an inflatable boat carrying 55 Africans, seven of them women and six chidren, was rescued by the Spanish coast guard off the Spanish coast.
A refugee holds two children as dozens arrive on an overcrowded boat on the Greek island of Lesbos
A child, covered by emergency blankets, reacts as she arrives, with other refugees and migrants, on the Greek island of Lesbos, At least five migrants including three children, died after four boats sank between Turkey and Greece, as rescue workers searched the sea for dozens more, the Greek coastguard said
Migrants wait under outside the Moria registration camp on the Lesbos. Over 400,000 people have landed on Greek islands from neighbouring Turkey since the beginning of the year
The bodies of Christian refugees are buried separately from Muslim refugees at the Agios Panteleimonas cemetery in Mytilene, Lesbos
Macedonian police officers control a crowd of refugees as they prepare to enter a camp after crossing the Greek border into Macedonia near Gevgelija
A refugee tries to force the entry to a camp as Macedonian police officers control a crowd after crossing the Greek border into Macedonia near Gevgelija
Refugees are seen aboard a Turkish fishing boat as they arrive on the Greek island of Lesbos after crossing a part of the Aegean Sea from the Turkish coast to Lesbos
An elderly woman sings a lullaby to baby on a beach after arriving with other refugees on the Greek island of Lesbos after crossing the Aegean sea from Turkey
A man collapses as refugees make land from an overloaded rubber dinghy after crossing the Aegean see from Turkey, at the island of Lesbos
A girl reacts as refugees arrive by boat on the Greek island of Lesbos after crossing the Aegean sea from Turkey
Refugees make a show of hands as they queue after crossing the Greek border into Macedonia near Gevgelija
People help a wheelchair user board a train with others, heading towards Serbia, at the transit camp for refugees near the southern Macedonian town of Gevgelija
Refugees board a train, after crossing the Greek-Macedonian border, near Gevgelija. Macedonia is a key transit country in the Balkans migration route into the EU, with thousands of asylum seekers - many of them from Syria, Afghanistan, Iraq and Somalia - entering the country every day
An aerial picture shows the "New Jungle" refugee camp where some 3,500 people live while they attempt to enter Britain, near the port of Calais, northern France
A Syrian girl reacts as she helped by a volunteer upon her arrival from Turkey on the Greek island of Lesbos, after having crossed the Aegean Sea
Refugees arrive by boat on the Greek island of Lesbos after crossing the Aegean sea from Turkey
Beds ready for use for migrants and refugees are prepared at a processing center on January 27, 2016 in Passau, Germany. The flow of migrants arriving in Passau has dropped to between 500 and 1,000 per day, down significantly from last November, when in the same region up to 6,000 migrants were arriving daily.
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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