They remained in custody for questioning on Monday.
While the woman is yet to be formally identified, her family have been informed, according to South Yorkshire Police.
Assistant Chief Constable Colin McFarlane said: “This is a devastating incident which has resulted in the death of a young woman while on a night out during the bank holiday weekend in Sheffield.”
He added police would continue to have a “significant presence at the scene in the area today and in the coming days”, and urged anyone with information to come forward.
“Now is not the time to stay silent,” he said.
“Bank holidays are one of the busiest times of the year, and we know that there were people in the area around West Street and Eldon Street who saw what happened or know who is responsible.”
West Street is closed between Mappin Street and Westfield Terrace, and Eldon Street, Westhill Lane and part of Orange Street have also been closed.
Drivers have been advised to avoid the area.
