Thames Valley Police have launched an appeal for witnesses after the public order incident.
The incident happened when two men were involved in an altercation in West Bar Street. The incident occurred earlier this week between 12.45am and 1.30am on Tuesday June 1.
One of the men suffered cuts and bruising to his face that required hospital treatment. He has since been discharged.
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It is believed that a dark blue Vauxhall Astra may have been used during the incident.
A 23-year-old man and a 24-year-old man, both from Banbury, were arrested in connection with this incident.
The 23-year-old man was arrested on suspicion of affray.
The 24-year-old man was arrested on suspicion of of affray, driving a motor vehicle when alcohol level above limit, criminal damage, breach of bail, being concerned in supply of a class A drug and possession of an offensive weapon.
They have both been released on bail.
Investigating officer, PC Robbie Wilson, based at Banbury police station, said: “I am appealing for anyone who may have witnessed this incident to please come forward.
“Anyone with information can contact the police by making a report online, or calling 101, quoting reference 43210236734.
“Alternatively, if you wish to remain anonymous, you can contact the independent charity Crimestoppers, on 0800 555 111 or via their website.”