Philadelphia Mayor Cherelle Parker adds that "many people on the ground" were injured as homes and fires in the areas were ablaze in the aftermath.
The medical transport plane was taking the girl - who had been receiving care in the US for a life-threatening condition - back to Tijuana, Mexico. Four crew members were also on board.
Flight logs show the plane was in the air "for only a minute before it crashed".
In an audio recording obtained by CBS News, the BBC's US partner, an air traffic controller can be heard saying they're "not exactly sure what happened".
One of the people hurt in Friday night's crash was a child who was hit by debris while sitting in a car, NBC News reports.
The child had surgery at Jefferson Torresdale Hospital and has now been moved to a children's hospital, the reporter says.
A number of people who were injured stayed in hospital overnight, while others were admitted and later released.
Videos of the crash show the plane coming down quickly and sparking a huge fireball.
Witnesses described shrapnel damaging cars and sending burning debris into the streets. Photos of the aftermath show burning, mangled cars.
One man who spoke with CBS, the BBC's US partner, said he was driving when he heard a whirring sound and then a loud explosion.
"Everyone just started screaming," he said.
"I saw blinking lights coming from the sky. And I just saw them going down," a 10-year-old boy told CBS on his way home from hockey practice. "It was really scary."
One witness told local media that the explosion "lit up the whole sky".
"I just saw a plane basically hit the building and it exploded. The sky lit up and I pulled over and basically, it was just real bad around here," the witness told WPVI-TV, external, describing the crash as feeling like an earthquake.
Ryan Tian, 23, told The Philadelphia Inquirer, external that he was getting dinner when he saw a "massive fireball" that turned the sky orange.
"I thought we were getting attacked by something," he said.
The Mexican consulate in Philadelphia says it has been in touch with the families of the people who died in the crash.
In a post on X, it adds that "the necessary consular assistance is being provided and work is being done with the authorities to clarify what happened."