The youngest child was an infant and the oldest was 3 years old, WTVM-TV of Columbus reported.
The mother was identified as Jerrica Spellman, the report said.
The circumstances leading to the deaths were not immediately clear but the bodies were found on a mattress inside the apartment, police told the station.
There was no immediate indication that a suspect had been identified in connection with the case.
This is a developing story. Check back for updates.