South Central Ambulance Service NHS Foundation Trust said on Twitter that one patient is being assessed and treated for "non-life threatening injuries".
Eyewitnesses described hearing the gunshots ringing out during the afternoon. There were reports the suspect was shooting from a balcony.
Janet Borgerson was in the nearby Hotel Malmaison when she heard "explosive cracks" she thought were holiday festivities before another series of "loud bangs".
"Again, I thought the second round were firecrackers. I noticed hotel bar staff ushering people inside," she said.
Borgerson, who is visiting the city from America, said guests were later told they were "perfectly safe" and allowed to leave the hotel by an armed officer who seemed to indicate he was expecting a siege.
A nearby resident, who did not want to be named, said he first heard two loud bangs early in the morning, but thought it was just Bank Holiday fireworks.
Later that day, he said he witnessed the start of the altercation between an armed man and the police, during which he heard around 20 shots exchanged.
He said: "I could hear a female negotiator and an armed response man trying to get him to put his hands up, let go of the gun, keep his hands on show and things like that."
The resident said he heard a man repeating that he needed medical treatment, before getting "really angry, shouting, roaring at them (the police)".
He said the whole street had been evacuated and families were getting anxious about where they would be able to spend the night as darkness fell local time.
A spokesman for Thames Valley Police said: "Our officers remain in Oxford city centre tonight working to resolve the ongoing situation".
