Police officers were alerted to a disturbance in Lyons Road, Pitsmoor, just after midnight yesterday and around 30 minutes later a man arrived at the Northern General Hospital with stab wounds.
Detectives investigating the stabbing believe it took place in Lyons Road.
The victim remained in a critical but stable condition last night.
A 32-year-old man was arrested on suspicion of attempted murder.
Last Saturday afternoon, a 21-year-old man was stabbed on neighbouring Lyons Street.
He remained in hospital in a stable condition yesterday.
Officers alerted to that incident also found evidence that a gun had been fired in the street.
Police patrols have been stepped up in the wake of the attacks.
Detectives believe the incidents are not linked.
Anyone with information should call South Yorkshire Police on 101 and quote incident number 4 of July 10.