Five suspects, including a policeman and a quarantine officer, were arrested for allegedly facilitating their travel, the government agency fighting trafficking says.
The victims were found while trying to board a plane from Lagos to Moscow.
They had football supporter ID cards in order to look as though they were fans heading to the World Cup in Russia.
The children, who were unaccompanied, are now in a shelter for victims of trafficking which run by the National Agency for Prohibition of Trafficking in Persons (Naptip).
Five other potential victims, also children, were stopped from boarding a flight to Russia when staff noticed they had one-way tickets.
Criminals have been pressurising young Nigerians and their parents to take advantage of the World Cup to get Russian visas, Naptip says.
It warns that, once out of the country, the victims would be exploited by traffickers.
Many victims of trafficking from Africa to Europe come from Nigeria.
According to the UN's agency for migration, most of the potential sex trafficking victims arriving in Italy by sea are Nigerian.