The disturbing incident started when an SUV was boxed in by a group of motorcyclists on New York City's West Side Highway.
"People come in with the apparent intent to be disruptive. That causes problems for the police department. That causes problems for everyone," said NYPD Police Commissioner Ray Kelly.
In a clip posted on YouTube, one biker suddenly slowed down in front of the Range Rover and the two collided.
The motorcyclists, 20 to 30 in all, came to a halt. Police say some of them started damaging the SUV. The 33-year-old SUV driver, Alexian Lien, accelerated to escape, running over 32-year-old cyclist Edwin Mieses.
"All his ribs are fractured. His lungs are so badly bruised that he's still on the ventilator," said Mieses' mother, Yolanda Santiago.
Lien was traveling with his wife and 2-year-old daughter. Apparently fearing for the lives of his family, he took off.
"My husband got off his bike to help the guy. And whatever he did, he got scared, he peeled off and paralyzed my husband on the way," said Mieses' wife, Dayana Mieses.
The motorcyclists pursued the SUV. The chase ended when Lien exited the freeway and got stuck in traffic.
The video shows one biker using his helmet to smash the driver's window. Authorities say the driver was pulled from the vehicle and beaten in front of his wife and child. Officials said he needed stitches to his face at a hospital. His wife and child were not injured.
"I don't condone the violence. There was no need for it, but he left," said Margie Mejia, Mieses' sister-in-law.
Police believe some of the motorcycle riders belong to a gang known as Hollywood Stuntz.
"We had over 200 calls just on Sunday about this group operating in a reckless manner," said Kelly.
Christopher Cruz, the 28-year-old motorcycle rider who initially slowed down in front of the SUV, has been arrested. Another man turned himself in for questioning on Tuesday. Police distributed an image of two bikers they said were involved in the chase and said they were wanted for assault.
Police have charged Cruz with reckless endangerment, reckless driving, endangering the welfare of a child and menacing. The driver of the SUV involved has not been charged. But authorities said Tuesday that they are still investigating the incident.
The Associated Press contributed to this report.