Armed officers, police dog units and neighbourhood police scoured the city centre and two police forces combined to arrest a man following the incident that led to Park Street off Leeman Road being closed for part of the afternoon.
Three men were seen fighting in Leeman Road at 2.19pm and an eyewitness reported seeing a weapon with a blade.
When police arrived shortly afterwards, they found two injured men.
Both were taken to hospital by land ambulance.
A police statement said: “An extensive search was launched immediately across York city centre to trace the suspect. This involved armed officers, police dog units and neighbourhood policing officers.
“As a result of swift enquiries in York, with the support of Humberside Police a man was arrested at Hull Railway Station later this afternoon.
“He was arrested on suspicion of serious assault and possession of an offensive weapon in public place. He is currently in police custody.”
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A cordon remained in place on Park Street for most of the afternoon.
The road has since opened to the public, but police are still maintaining a reduced cordon while they continue their investigation.
They are appealing to anyone who witnessed the incident, or who has relevant CCTV, dashcam or mobile phone footage, to contact North Yorkshire Police on 101 and quote reference 12260200081.