Ágatha Vitória Sales Félix was with her mother in a van when she was shot in the back in a poor area on Friday.
Residents said officers had targeted a motorcyclist when she was hit. Police said they had responded to an attack.
A record 1,249 people have died in such raids in Rio from January to August.
Ágatha is the fifth child to die as a result of violence blamed on the police this year.
Critics say the hard-line approach of Governor Wilson Witzel, who came to office in January, is behind the growing number of victims in the city's poorest areas - favelas - many of them controlled by powerful drug gangs.
Ágatha was going back home with her mother on Friday night in a van when she was shot in the back in Alemão, one of Rio's largest favelas. She was sent to a hospital but died.
In a statement, police said officers had responded to attacks from criminals, which led to a confrontation. An investigation has been launched.
But Ágatha's family disputed this, saying officers had targeted a motorcyclist that was passing nearby when she was hit, and there was no gunfight happening at the time.
"A guy came on a motorbike and the police asked him to stop. He didn't stop and left, he was unarmed, and the police shot. There was no confrontation, the only shot was [from the police]," the girl's uncle, Elias, told local media.
Her grandfather, Ailton, said: "They [authorities] will say that a child died in a confrontation. What confrontation? Was my granddaughter armed?"