The Israeli army confirmed on Wednesday that it had fired at the house of a weapons dealer in the southern town of Rafah, on the Egyptian border.
The army said that it warned the owner of the house 15 minutes before the initial air strike happened.
But the 14-year-old girl was killed when she and other children gathered around to look at the rubble when a second Israeli missile landed, witnesses said.
Doctor Ali Musa, director of Rafah hospital, said 10 other people were wounded by the blast, most of them women and children who suffered broken bones, bruises and shrapnel wounds.
The Israeli strike came hours after a rocket fired from Gaza wounded an off-duty Israeli soldier in the southern Israeli town of Sderot.
The air strike came as an Israeli human rights group accused the army of war crimes for bombing Gaza's only power plant at the start of a major military offensive.
Israel has stepped up military operations in Gaza, a coastal strip it had withdrawn from last year, after Palestinian fighters captured a soldier in a June 25 cross-border raid.