The family produced a birth certificate and passport for the child, but neither was accepted as conclusive proof of her birth.
The authorities have ordered DNA tests to be undertaken in order to establish whether the couple are the child's biological parents.
About 20 members of the Roma community in Dublin gathered outside the city's family law court yesterday while a hearing took place to establish a care order for the child.
The Health and Safety Executive sought an emergency order under Section 13 of the Child Care Act 1991 after requests from police.
The emergency order could result in the child remaining in care for up to 28 days while the situation is examined. No arrests have been made and there is no allegation of abduction against the family.
The girl was said to be physically well.
Suspicions were apparently raised because the girl was blonde with "striking blue eyes", whereas every other member of the family had dark complexions.
The case comes just days after a blonde girl, believed to be aged 5 or 6, who had been living with a Roma family in Farsala, Greece, was taken into care when DNA tests proved she was not their biological daughter.
Christos Salis, 39, and his wife Eleftheria Dimopoulou, 40, have been held on charges of abduction and document fraud.
Greek police are examining the possibility that child traffickers had planned to sell the girl, known only as Maria, to a wealthy family but placed her in a gypsy camp as police moved in on them.
The couple at the centre of the case insist they took the girl into their care when her mother handed her over shortly after the birth.
Greek police confirmed that DNA tests have shown Maria cannot be any of the missing children on a list provided by Interpol.
They are now seeking help from anthropologists in an attempt to determine her likely origins based on her characteristics. Smile of The Child, the charity put in charge of Maria's welfare, has said she will formally be put up for adoption in six months if her biological parents are not found.
The case has raised the hopes of families of missing children such as Ben Needham and Madeleine McCann.