Emergency services were called out to reports of a disturbance in Ballifield Drive, Handsworth, at about 3pm on Friday, June 21.
A video taken by a witness has since emerged showing how the fight unfolded.
There is a scuffle between two men and a woman before one of the men appears to be hit by the other with a plank of wood.
Police confirmed a 40-year-old man was working in an area close to the Premier convenience store when he was attacked.
A woman was also injured in the altercation. Both sustained minor injuries that did not require treatment.
Police arrested a 50-year-old Sheffield man on suspicion of grievous bodily harm, while another man believed to have been involved fled the scene.
The force today revealed nobody has been charged in connection with the incident and enquiries remain eongoing to locate the wanted man.
Shortly after the attack, Detective Sergeant Andy Shields, who is leading the investigation, said: “We understand that this kind of incident is very disturbing for those who may have witnessed it or live in the local area.
“I would like to offer my reassurance that there is no risk to the wider public as it is my belief that this was a targeted attack.
“As this assault took place when there were a number of young people in the area due to it being the end of the school day, I’m keen to hear from anyone who has mobile phone footage of what happened.
“It may be that you can help us identify the man who left the scene and ensure that we are able to progress our investigation.
“If you were in the area and have mobile phone footage, have caught something on dashcam or have your own CCTV that may help please get in touch.”
Anyone with information about the incident is asked to contact police on 101 quoting Incident number 516 of 20 June.