It happened at around 5:30 p.m., at West 33rd Street and Seventh Avenue, police said.
Two women and a man were taken to Bellevue Hospital in New York City with non-life threatening injuries. The driver remained at the scene, law enforcement officials said.
The incident caused some panic in the area; a witness said the van was dragging pedestrians before stopping near West 31st Street. Bystanders hastily went to help the injured, according to reports from the scene.
The NYPD said that the van's accelerator pedal may have gotten stuck. An investigation is underway.