Emergency services were called to Oaks Lane, Hoyle Mill, at around 8.30am following reports that a silver Kia Rio had been involved in a collision with a pedestrian.
The vehicle had been travelling in the direction of Pontefract Road when it is reported to have mounted the pavement and collided with the pedestrian who was walking his dog, close to Barnsley Main Colliery.
The pedestrian, a 32-year-old man, and the dog, were pronounced dead at the scene.
A police spokesman said: “We are asking anyone who saw the collision, who saw the car prior to the collision, or who may have dashcam footage, to contact us.
“We would also like to speak to anyone who stopped to help at the scene.”
Contact 101 quoting incident number 150 of January 13.