The man is suspected of smashing the driver's window of the sport utility vehicle, a law enforcement official knowledgeable about the investigation told CNN Thursday.
The incident, a video of which went viral, occurred Sunday on Manhattan's West Side Highway.
Police said the SUV, driven by Alexian Lien, hit a motorcyclist who had slowed. The SUV pulled over and was surrounded by other bikers, members of the motorcycle group Hollywood Stuntz, who hit the vehicle, invesigators said.
When the driver pulled away, the SUV hit three more bikers, including Edwin Mieses, who was critically injured.
The bikers gave chase, surrounding the vehicle when Lien was stuck in traffic. The video shows the biker who is sought by police using his helmet to smash the window.
Police said the bikers pulled Lien from the vehicle and beat him but did not harm his wife and daughter. Lien was treated at a hospital for facial injuries.
In a statement issued Thursday through an attorney, Lien's family said he was "forced under the circumstances to take the actions that he did in order to protect the lives of our entire family."
Police have not indicated whether they would file charges against Lien.
Police said they arrested one biker and released another when they determined he was trying to help, CNN said.
Police said they were searching for other potential suspects.
Mieses' wife, Dayana, told WBZ-TV, Boston, he was trying to help the SUV driver.
"And whatever he did, he got scared, he peeled off, and he paralyzed my husband on the way," she said.