The 20-year-old was held on suspicion of possession of a firearm or imitation with intent to cause fear of violence after police received reports of a shooting outside a block of flats in Batemoor last week.
Police officers were deployed to the city estate in the early hours of Friday, July 9 after reports of a suspected shooting.
Batemoor Road was sealed off between Whinacre Close and Dyche Lane while enquiries were carried out.
Nobody is believed to have been injured in the incident, which is still under investigation.
The man arrested by officers has been released under investigation.
South Yorkshire Police said members of the public ‘reported hearing shots fired outside a block of flats’.
Detective Chief Inspector Paul Murphy, from the Armed Crime Team, said: “We will continue to do all we can to keep illegal weapons off the streets of South Yorkshire.”