A Reuters witness said one person was covered with a bloodstained blanket after the collision, which occurred around noon ET (1600 GMT) at the Midtown Manhattan tourist venue.
Hundreds of thousands of people, many of them visitors from around the world, pass daily through the bustling commercial area, the heart of the Broadway theater district.
The vehicle was a red Honda sedan and CBS New York Television said the driver had been removed. Television footage showed police officers restraining a man in a dark T-shirt and placing him in a police car.
Witnesses said the motorist had driven against traffic and onto the sidewalk, striking pedestrians.
“Everybody was just running, everyone was concerned for their lives,” a witness told local CBS.
The car crashed into a pole and came to rest at 45th Street and Broadway.
Seven people were being placed on stretchers, a Reuters witness said. Shoes were scattered at the scene and one person was covered by a bloodstained blanket, the Reuters witness said.