Medunjanin's attorney, Robert Gottlieb, said investigators were looking to seize his passport.
Law enforcement sources said a surveillance team was following Medunjanin, who they said rear ended another vehicle at the Whitestone Expressway and then attempted to flee the scene.
Medunjanin was charged with leaving the scene of an accident.
He was treated for injuries sustained in the accident at New York Hospital Queens, police said.
In an interview outside his apartment in September, Medunjanin told Eyewitness News reporter N.J. Burkett that he would be surprised if Najibullah Zazi were part of a terror plot.
"The Najib I know, I never seen any of those signs," he said.
Zazi was arrested last September on charges of plotting to carry out acts of terrorism against the United States.