Neveah Benson was shot at about 1:45 p.m. Saturday, The (Cleveland) Plain Dealer reported. She was transported to a local hospital where she later died.
Neveah shot herself, police said, but it was not clear how she got the gun.
Her father, Edmund Benson, 23, was arrested following the shooting on suspicion of child endangering and having a gun after a felony conviction.
Benson is prohibited from owning guns after felony convictions for receiving a stolen vehicle and possessing criminal tools in 2009 and failure to register his address when he lived in Shaker Heights in 2008.