The incident happened at 71st Street and Grand Avenue in Maspeth around 7:50 a.m.
All the children are reportedly students at IS 73Q, Frank Sansivieri Intermediate School, which is in the vicinity. PS 58 The School of Heroes is also nearby. They were all 12 or 13 years old.
Police say the driver accidentally stepped on the gas instead of the brakes, careening onto the sidewalk and flattening a parking meter and a sign before hitting the kids.
One of the victims suffered a serious leg injury and was rushed to Elmhurst Hospital, officials said.
"I hear one of the girls screaming," student Elija Bruce said. "She was on the floor with her knee on the floor, screaming that she couldn't move her leg."
Lynx Garcia was driving at the time and saw the accident unfold. She jumped from her vehicle to help.
"He went up over the curb and ran right into the kids coming out of the store," she said. "I saw one of the girls under the car, and I helped get her out. I held her until they came."
David Foubister, who was walking his dog, also rushed to help.
"Me and like 10 other guys helped lift the car up, and that was it," he said. "We got the girls out, and from there, paramedics and police and everybody was here after that."
The five students were taken to Elmhurst Hospital to be treated for their injuries, none of which were believed tob e life threatening.
The driver stayed at the scene and was later given a Breathalizer test by police.
"I think he was in shock," Garcia said. "He had his own child, a little girl, in the car, and he didn't even go to the back. He just stood there."