The incident happened at around 1.50am on 15th November on Swallow Wood Road at the junction with Haigh Moor Way in Swallownest.
A spokesman for South Yorkshire Police said that the injured man and three male friends had travelled in a black Hackney cab, believed to be a Peugeot Expert.
They had got into the cab at a taxi rank outside the Corporation nightclub in Milton Street, Sheffield.
When the group reached Swallownest it appears the 20-year-old local man fell from the moving taxi.
As a result of the fall, he suffered fractures to the skull around his right eye socket.
The injured man was taken to Rotherham Hospital for treatment, where he remains.
The police spokesman said that it was likely he would be transferred to Sheffield’s Royal Hallamshire Hospital for surgery at some point.
In the meantime, another of the passengers paid the taxi driver the fare and the taxi left the area.
Officers are appealing for anyone who may have witnessed the incident to get in touch with them.
They would also like to speak to the taxi driver who took the group home from Sheffield city centre in the early hours of Thursday 15th November.
Anyone who witnessed the incident or who has any information, is asked to call South Yorkshire Police on 101, quoting incident number 387 of 17th November 2012.
Alternatively, people can call Crimestoppers, anonymously, on 0800 555111 and leave a message for officers.