Biker Nicholas Robinson suffered a broken hip and multiple bone fractures after his cycle was in collision with a van near his home in Clay Lane.
Mr Robinson, 64, was on his way to work when the incident occurred on the Clay Lane West roundabout on Barnby Dun Road on March 19.
His nephew Mark Hunston said: "It is a busy road round there, so someone must have seen what happened.
"It was a pretty nasty accident and he's been left in a bad way. I can't believe they just drove off afterwards."
Emergency services were called at around 3.50pm following reports of the collision.
A South Yorkshire Police spokesman confirmed that a cyclist and a white van were involved in the collision.
The spokesman said: "The cyclist is reported to have suffered serious injuries, mainly a broken hip in the incident. The van reportedly failed to stop at the scene and enquiries are ongoing to trace the van and any witnesses to the collision."
Anyone with information should call 101 quoting incident number 641 of 19 March 2018.