The incident happened in Stubbin Lane, Firth Park just after 5.45pm on Saturday evening, and resulted in a man being taken to hospital to be treated for a cut to the head.
A South Yorkshire Police spokesman said: "We were called to Stubbin Lane on Saturday at 5.46pm by a member of the public who believed someone had been hit on the head with a brick.
"When officers arrived, they found there had been a minor assault but there was no mention of a brick or any other weapon being used.
"A male attended Northern General Hospital with a minor cut to the head.
"It was reported that someone had a quad bike stolen from the Attercliffe area three days earlier and the victim of that theft spotted what he believed to be his quad bike being ridden around the area.
"The owner of the stolen quad bike is said to have given chase to the quad bike, which had a male passenger riding pillion.
"The driver pulled up and there was a very minor assault in which the driver was injured.
"We had a number of calls from members of the public. There was some concern that there had been a collision involving a quad bike and a 4x4 vehicle driven by a man whose quad bike had been stolen, but that proved not to be the case.
"Investigations are ongoing and no arrests have yet been made."
South Yorkshire Police did not provide any further information, such as the ages of the people involved in the incident.
Anyone with information should call South Yorkshire Police on 101.