The crash happened on Thursday evening at 7.30pm but West Yorkshire Police has only today released details.
Two pedestrians, a 66-year-old man and a 67-year-old woman, were taken to Pinderfields Hospital after the incident on James Street.
"A red BMW 316 was travelling along the A638 High Street in Heckmondwike, in the direction of Dewsbury," police said in a statement.
"It made a right turn onto St James Street, near to the Travellers Pub and a collision occurred between the car and two pedestrians.
"The driver of the BMW stopped at the scene."
Police are now appealing for any witnesses to get in touch. Anyone with information is asked to call 101 quoting reference 1683.