Police are investigating two incidents in the Swan Lane and Beatrice Street areas of the town that they believe are linked. Two men were arrested.
Emergency services say the disorder happened on Monday evening.
A spokesman for West Midlands Ambulance Service said: "We were called to reports of a stabbing on Beatrice Street at 8.17pm and sent one ambulance to the scene.
“On arrival, we discovered one patient, a man, who was treated for injuries not believed to be serious before being taken to hospital for further assessment.”
Half an hour earlier police went to nearby Swan Lane.
West Mercia police said: "At 7.45pm we were called to an incident on Swan Lane, Oswestry following reports of a disorder involving a group of individuals.
"We then received a second call to Beatrice Street just before 8pm following further reports of a disorder outside the BP garage. Two men aged 18 and 43 were then arrested at the scene on suspicion of affray. We believe the two incidents are linked.
"Anyone who has any information is urged to call 101 or visit our website, quoting incident 599i of 20 September 2021 or report it online via our website.
"Alternatively, if you have information but don’t feel comfortable speaking to police, you can speak to the independent charity Crimestoppers. It is 100 per cent anonymous, they never ask your name and they cannot trace your call or I.P address. You can contact them online or by calling 0800 555 111."