Emergency services were called to Margate Drive, Pitsmoor, at around 9.35pm on Tuesday after a gun was fired at a taxi which pulled into the street for a pre-booked fare.
A gun was fired from a blue Audi A3 which pulled up alongside the taxi before it left the scene.
The taxi driver escaped unharmed but detectives believe there is a possibility that one or more of his three passengers – men in their 20s – were hurt.
Last night the passengers had still not come forward.
A 23-year-old Sheffield man arrested on suspicion of firearms offences has been bailed until November 22.
Anyone with information should call South Yorkshire Police on 101 and quote incident number 892 of October 29 or Crimestoppers, anonymously, on 0800 555111.