Europol said thousands of vulnerable minors had vanished after registering with state authorities.
It warned of children and young people being forced into sexual exploitation and slavery by criminal gangs.
Save the Children says some 26,000 child migrants arrived in Europe last year without any family.
It is the first time Europol has given a Europe-wide estimate of how many might be missing.
What happens to lone child migrants?
Migration to Europe explained in graphics
“It’s not unreasonable to say that we’re looking at 10,000-plus children,” Europol’s chief of staff told the Observer newspaper.
“Not all of them will be criminally exploited; some might have been passed on to family members. We just don’t know where they are, what they’re doing or whom they are with.”
Officials in Italy warned in May 2015 that almost 5,000 children had disappeared from asylum reception centres since the previous summer.
The BBC’s Katya Adler heard how migrant boys in Rome sold sex in order to survive
Confirming the overall estimate of missing minors, a Europol spokesman said a large proportion may have also disappeared after landing in Greece. The country is the first entry point for most of the 1 million migrants who arrived in Europe by boat in 2015, and authorities have been criticised for failing to register and check the arrivals.
Criminal gangs known to be involved in human trafficking in Europe are now targeting refugees, Europol said.
There are fears unaccompanied children and young people may be dragged into sex work, slavery and other illegal activity.
The International Organization for Migration (IOM) spokesman Leonard Doyle told the BBC the figure of 10,000 missing children was “shocking but not surprising”.
He said it was “to be expected” that many of these would be caught up in exploitation.
“Let’s hope now the EU puts the resources into finding these children, helping them and reuniting these children with their families.”
Exploited and abandoned
The BBC’s Europe editor Katya Adler exposed the plight of vulnerable children arriving in Italy in an investigation last year. Here is an extract:
Many Nigerian girls are told they must pay traffickers thousands of euros or their families will be harmed Fabio Sorgoni works for the Italian charity On The Road. He told me that there is a very short window of time to provide unaccompanied minors arriving in Europe with a safe haven.
By law, they are allowed out of reception centres during the day, when they easily fall prey to organised crime or individuals looking to exploit them, he said.
Few Italian centres have enough translators who speak the children’s languages. They do not employ staff experienced in spotting victims of sexual exploitation.
Feeling uncertain and unprotected, thousands of children have run away from Italian reception centres, disappearing on to the streets.
With no one stepping in or taking responsibility for them, they’re left to fend for themselves – doing what it takes to survive.
The warning from Europol comes days after the UK government said it would accept more unaccompanied child refugees from Syria and other conflict zones, without giving numbers.
However, it said it would not be taking in vulnerable children who had already made it into Europe.
On Saturday, at least 39 migrants, including several children, drowned trying to cross the Aegean Sea from Turkey to Greece.
The IOM said on Friday that 244 migrants had drowned in the Mediterranean so far this year, out of 55,568 arrivals.
A note on terminology: The BBC uses the term migrant to refer to all people on the move who have yet to complete the legal process of claiming asylum. This group includes people fleeing war-torn countries such as Syria, who are likely to be granted refugee status, as well as people who are seeking jobs and better lives, who governments are likely to rule are economic migrants.