Authorities in the small southern city of Lebrija also arranged a doctor's appointment to make sure the young mother and infant are doing well.
In a statement, city officials said they are investigating when the pregnant child arrived in Spain and why she had not seen a doctor before showing up last week at a hospital to give birth.
Authorities did not give details about the modest apartment where the 10-year-old girl is now living with her mother, but the mayor of Lebrija called it "humble."
Officials have said they could step in to oversee care of the girl and her baby if needed, but, but the statement Thursday did not reveal whether any problems were found or the results of the medical appointment.
City officials "will guarantee the protection of the two minors," the statement said.
The birth has shocked Spaniards and created an international sensation.
The girl's mother told reporters earlier this week that she's delighted to have a new granddaughter and doesn't understand the fuss the birth has caused. She said the baby's father is a 13-year-old boy who is still in Romania.
She also said since they are Romanian Gypsies, or Roma, it is their custom to marry very young.
Arranged "marriages" for girls reaching puberty are relatively common among Roma, who make up about 1.5 million of Romania's 22 million people. Those marriages are not recognized by the state, which requires girls to be 16 and have parental consent before they can marry.
Alan Clendenning in Madrid contributed.