Medical sources said that the Saturday evening aerial attack came in the neighbourhood of Shajaya, near the Karni border crossing on Gaza's eastern border with Israel.
Hospital officials said six people were wounded.
The Israeli army confirmed an air strike in the area, but denied hitting any homes.
"An air strike targeted a group of gunmen walking in an open area near the Karni crossing. We did not hit any buildings," a spokesman said.
The little girl, Rawan Hajaj, was carried inside a Gaza City hospital, wrapped in a red blanket. The back of her head was sheared open, and her legs dangled lifelessly.
At the hospital, doctors bandaged the head of a trembling, blood-covered young boy, and treated a man whose right arm was almost completely torn off.
A neighbour said he ran to the girl's house after hearing the blast.
"People were sitting under a tree outside the house when the explosion occurred," said Sakr Hajaj.
He described the scene as a "bloodbath", with body parts strewn around, and children screaming.
The courtyard outside the house was stained with blood, and a pool of blood collected near the front door. One of the house's walls was torn open by the force of the blast.
In another air strike, an Israeli aircraft targeted a group of Palestinian fighters in western Gaza City early on Sunday. At least three people were wounded, one seriously, Palestinian hospital officials said.
Earlier on Saturday, another four Palestinians were killed in sporadic exchanges of fire with Israeli forces who took up positions overnight in nearby farmland and industrial areas.
Forty Palestinians have been killed since Israel launched its massive military operation in Gaza late on Wednesday.
One Israeli soldier was also killed in the operation which is aimed at suppressing rocket attacks and freeing a captured soldier.