Police taped off an area at the back of The Moor Market while forensic officers were also seen close to South Yorkshire Fire and Rescue's headquarters in Eyre Street.
Police have now arrested a 24-year-old man in connection with the reported stabbing which left a 22-year-old man in hospital with non-life threatening wounds.
A force spokesperson said: "At around 5.15am on Saturday, December 16, emergency services were called to Eyre Street, Sheffield, following reports a man had been found with injuries.
"A 22-year-old man was taken to hospital with suspected stab wounds, which are not thought to be life-threatening at this time.
"A 24-year-old man has been arrested on suspicion of attempted murder and remains in police custody being questioned by officers.
"Enquiries are ongoing."
A witness, who took pictures of the scene, said earlier: "Market staff say they found a man stabbed when they arrived first thing. It's business as usual inside and all the other entrances are open."