The Ingham County Sheriff says the 5-year-old girl died of trauma before the fire.
Sheriff Gene Wriggelsworth tells us a 25-year-old male is in custody.
He says the suspect and victim were the only ones in the house at the time of the fire.
The mother of the child was at work.
Police are waiting for autopsy results to determine a cause of death.
More details on the investigation are expected to be released Thursday.