Asif Malik, 31 and Sara Kiran, 29, were arrested in Turkey two weeks ago after British police appealed for information on their whereabouts.
The pair and their children, who are under seven, were reported missing from their home in Slough on 16 April.
They were deported from Turkey on Tuesday and moved to Moldova.
"We can confirm the detention of a British family in Moldova," said a Foreign Office spokesman.
"We are working closely with UK and Moldavian authorities to help ensure their well-being. We will not comment further on cases involving minors."
The family left Slough, Berkshire, on 7 April without mentioning their travel plans to relatives.
They boarded a ferry from Dover to Calais a few hours later, before travelling through Europe and crossing into Turkey through Greece.
Last month, police said online rhetoric from Islamic State (IS), the family's direction of travel, and concerns voiced by relatives, made officers "concerned" that they were heading for Syria.
Thames Valley Police also stressed that the family's disappearance was a missing persons' inquiry - not a criminal investigation.
A British couple believed to have been travelling to Syria with their four children have been detained in Moldova, the Foreign Office has said.