Hertfordshire Police Detectives are questioning a 30-year-old man from Hatfield on suspicion of murder.
The arrest comes after a four-year-old girl was found by police at an address in Hatfield, Hertfordshire.
It has been reported that the girl’s father, who won the right to keep the child in a custody battle, has been arrested.
The girl is said to have been living with her father since Christmas.
Police were called to the child’s home in Queen Bee Court, Hatfield, at 9.36am on Wednesday.
The child was in need of medical treatment and was taken to Lister hospital in Stevenage where she later died.
It is believed that there was nobody else in the house when the girl was found.
It is not yet known how the girl died. A post-mortem examination to determine exact cause of death will take place on Monday.