Pictures and video which have been posted on social media show a man walking down the street with a hammer last Wednesday evening at The Oval, in Firth Park, at one point, and also showed a person being kicked while on the ground by a group of people in the middle of the street.
Several people can be seen in the pictures.
The footage then shows police cars and several police officers arriving on the scene to deal with the situation, while shouting continues as the officers speak to people.
The woman who posted the pictures described the scenes as absolutely disgusting and said that a family was having to leave their home because of violence which had broken out.
South Yorkshire Police have confirmed that they had been called out to deal with the incident, and that they had made arrests.
Officers also appealed for information on the incident.
The force said in a statement: “Officers attended reports of disorder on Wednesday 15 June around 9pm at The Oval, Firth Park in Sheffield.
“It is believed the households from two properties were involved in a verbal and physical altercation.
“One man aged 50, two men aged 18 and one women aged 18 were arrested on suspicion of assault and public order offences. They have been released on police bail.
“Anyone with information is asked to call 101 quoting incident number 997 of 15 June 2022.”