Three unmarked police vehicles, with their lights and sirens on, were travelling 5 to 10 minutes ahead of the motorcade on Manhattan's West Side and were checking traffic before Biden passed en route to a television appearance on "The Daily Show with Jon Stewart," chief police spokesman Paul Browne said.
The cars were going through an intersection when the second one collided with a livery cab around 5:40 p.m. Traffic had stopped for the police, but the livery cab driver pulled out around the line of vehicles and was trying to go through the intersection, police said.
A passenger in the livery cab refused medical attention at the scene. The cab driver and two police officers were examined at a hospital and were released.
The police vehicles had been sent out as a routine patrol ahead of Biden, and the motorcade was not involved, Browne said.
Secret Service spokesman Darrin Blackford said the motorcade continued on its route to the Comedy Central channel show's studio, a few blocks from the accident site.
In another accident involving the vice-president this week, a sheriff's deputy was injured Monday in Albuquerque, New Mexico, when a woman drove around police vehicles blocking an intersection and collided with the deputy's car.
Biden had been in Albuquerque to speak at a campaign fundraiser for two New Mexico Democrats.