Shots were fired at the home Coun Mohammad Maroof, who is standing for re-election in the Nether Edge and Sharrow Ward, in Edgedale Road, Nether Edge, at around 3.20am on Tuesday.
A police cordon remained in place outside his home and that of three of his neighbours throughout the day.
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John Mothersole, Sheffield Council’s chief executive, said: “The alleged firearms incident this morning is clearly an act of criminality and the investigation into this is being dealt with by South Yorkshire police.
“At this stage, we do not believe there is any political motivation for the incident.”
Coun Jim Steinke, a fellow Labour ward councillor, said he had spoken to Coun Maroof and the police.
He said: “It’s inevitably worrying but it’s particularly worrying because he is standing for election and has a young family.
“He is obviously shaken up. We will be issuing a further statement later today.”
One neighbour said there have been a series of incidents at the property over the last few months.
He said a couple of months ago masked men pulled up and smashed the windows of a vehicle outside the house before dragging the owner out and breaking his arm.
He claimed that the windows of Coun Maroof’s home, which he shares with his family, were recently smashed with bricks and rocks.
Speaking about the latest incident, he said: "Just after 3am, I heard a bang and as soon as the bang went the car alarms went off.
“I thought somebody had hit a car it was that loud. I didn't hear any cars pull up so whether they were on foot I don't know.”
In a statement, South Yorkshire police said officers were called to a property in the Nether Edge area in the early morning after reports of shots being fired.
“Police attended the scene and found damage to a window consistent with shotgun discharge. The area was searched but the offenders could not be located,” the force said.
“Inquiries are ongoing and there is an increased police presence in the area as our officers continue their investigation.”
Police added no-one was injured in the incident.
The shooting came just hours after a man was found with a stab wound on nearby Abbeydale Road.
The injured man turned up at a restaurant with a stab wound under his arm at around 11pm and was taken to hospital for treatment.
Both the gunman and knife attack suspect remained at large as The Star went to press.
Anyone with information should call South Yorkshire police on 101, quoting incident number 111 of April 23.
Alternatively, call Crimestoppers, anonymously, on 0800 555111.