The collision closed one of the entrances to the airport for more than an hour, backing up traffic.
Police say the suspect stole the taxi at the Central Terminal Building just after 5 a.m. Friday.
Moments later, the cab crashed into a police van at the airport's 94th Street entrance.
The suspect was taken to Elmhurst Hospital. The two police officers in the van sustained minor injuries.
The 94th Street entrance to the airport was closed for the police investigation. Drivers were directed to the 102nd Street entrance or the entrance from the Grand Central Parkway.