Officers are still on the scene in Wensley Street, Firth Park and a cordon remains in place around three houses on the street.
It is understood that residents living on the street have been able to pass through the cordon, while members of the public are still being denied access.
A South Yorkshire Police spokesman confirmed that officers were called to the scene at 12.02am this morning, where the man was found with fatal injuries.
No information on the man's identity have been released at this time, and it is also not known whether any arrests have been been made in connection with the man's murder.
A South Yorkshire Police spokesman said: "We are appealing for information after the murder of a 31-year-old man on the Wensley Estate in Firth Park, Sheffield.
"Police were called at 12.02am on Sunday, September following reports that a man had been injured.
"He was taken to hospital but was pronounced dead shortly afterwards. A murder investigation has now commenced."
Anyone with information is asked to call police on 101, quoting incident number 3 of September 10, 2017.
You can also contact Crimestoppers anonymously on 0800 555 111.