The girl, who is not being named because of her age, went before a juvenile court judge Monday and was ordered to undergo a mental competency exam before her next appearance.
"We're trying to figure out what would motivate someone to do something like that," Wickliffe Police Chief Randy Ice told reporters. "And so far, we haven't come up with an answer."
The incident took place Friday at an apartment in the city of Wickliffe, about 17 miles outside Cleveland.
The girl's mother was babysitting the infant, Zuri Whitehead. She wanted to give the baby's mother a break from caring for a newborn, police said.
After the mother fell asleep on the couch, the girl took Zuri upstairs, Ice told the court at Monday's hearing. She returned 45 minutes later, woke the mother up and said something was wrong with the baby, Ice said.
Zuri was taken to a hospital where she died during surgery.
The baby had massive injuries to her brain, liver, spleen and kidney, Ice said.
The police chief said he is considering offering counseling for officers who responded to the scene.
"We're having a hard time getting our head around this," he told reporters. "You don't see something like this, hardly ever."
At the hearing, the little girl, all of 4-feet tall and about 50 lbs, appeared in leg shackles and sat beside her mother, as family members sobbed, CNN affiliate WOIO reported
The scene made even seasoned prosecutors well up, the affiliate reported.
A judge asked if she understood the charges against her. She answered yes.
She is being held at the Lake County Juvenile Detention Center.