Video shared by the governor's office shows Cuomo holding the man's left leg as he is helped down from the driver's seat of the vehicle. State troopers in Cuomo's security detail also helped.
The FDNY told the New York Post that no one was hurt.
The truck appeared to be on its side on the barrier dividing the east and westbound lanes.
The exact cause of the crash was unknown.
Cuomo's vehicle appeared to have been traveling in the opposite direction and was not involved in the incident.
He and his staff were heading to catch a flight after the governor spoke at the Association for a Better New York luncheon.