The 21-year-old was delivering parcels in Barnby Dun Road, Clay Lane, at around 2pm on February 17, when he is reported to have been hit by an orange Nissan Note.
The man was taken to hospital, but sadly died on Sunday evening, South Yorkshire Police have confirmed.
The driver of the Nissan stopped following the collision and is assisting police with their enquiries.
Officers are appealing for any witnesses to contact them as soon as possible.
A police spokeswoman said: "We are appealing to anyone who witnessed the collision, or who saw either party prior to the incident, to get in touch. Were you walking in Clay Lane or crossing the road at the time of the collision? Did you see what happened?
"If you can help, please get in touch. We are also keen to hear from anyone with dash cam footage."
Anyone with information can call police on 101 quoting incident number 429 of February 17.