Jarvin Blake, aged 22, was knifed at the junction of Brackley Street and Catherine Street, Burngreave, in an attack at 3.20pm yesterday afternoon.
Detectives believe a car pulled up and a number of people got out before chasing Jarvin and a friend and then stabbing them.
Jarvin was taken to hospital with stab wounds to his upper body but could not be saved.
A 23-year-old man injured in the same incident remains in hospital in a stable condition today.
Sheffield's District Commander, Chief Superintendent Stuart Barton, has issued a direct plea to those involved in the attack to hand themselves in.
He said Jarvin's family is devastated at the murder.
Detectives are said to be keeping an open mind over the motive for the attack.
Around 70 police officers, staff and detectives are working on the case.
Anyone with information should call South Yorkshire Police on 101 or Crimestoppers on 0800 555111.