The child was taken to hospital and was kept overnight following the incident which occurred at around 5.50pm on Thursday (July 21).
South Yorkshire Police said it was reported that a silver BMW was in stationary traffic on the Parkway, around half a mile from the Catcliffe turnoff, when it was involved in a collision with a grey BMW travelling out of the town centre.
The impact resulted in a third vehicle, a blue Honda Civic, colliding with the silver BMW and the grey BMW is reported to have collided with a fourth car, a grey Volkswagen Golf, which then clipped the side of a red Ford Fiesta.
The drivers of both BMWs were taken to hospital with minor injuries.
Officers would like to hear from anyone who saw the collision or the manner in which any of the vehicles were being driven prior to the collision.
Anyone with information should contact 101 quoting incident 882 of July 21.