A siege is under way as officers try to negotiate with the armed man.
Norfolk Road is in lockdown after shots were fired from a residential property in Paradise Square before armed response officers returned fire.
Members of the public have been warned to avoid the area, but police say the incident is not being treated as terrorism.
South Central Ambulance Service NHS Foundation Trust said on Twitter that one patient is being assessed and treated for “non-life threatening injuries”.
Armed response officers responded to a report shortly after 1.15pm on Monday that a man had access to a firearm, Thames Valley Police said.
Superintendent Joe Kidman said: “People in Oxford will notice an increased police presence in the area while officers are dealing with the incident, which is contained and taking place at a residential property.
“If you have any concerns or wish to raise anything please approach and speak to an officer or call the non-emergency number 101.”
The Westgate Centre is not within the police cordon and remains open as normal.
A woman, who asked not to be named, said she was sat on her balcony when she heard loud bangs, shouting and dogs barking on Monday afternoon.
“After a second round it became apparent these were gunshots so I rushed inside,” she told the Press Association.
“There was a couple more shots, three spurts in total, still a lot of shouting and barking. I heard a man shout ‘show me your hands’ repeatedly.
“The shouting continued and only quieted down an hour later or so, between now and then there have been bursts of shouting, barks and helicopters.
“I’ve heard no more shots since though. The entire area outside my flat is sealed off, and there is a police officer with a dog stationed a few metres from the 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 told the Press Association.
Ms 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.
She said: “Because the shooting was directly behind the hotel block in which my room is, I did feel worried that someone with a larger weapon could be a threat.
“But the police were quickly on sight and after 45 minutes or so inside, and then briefed by police, they seemed to have the shooter isolated.
“To the police after a short time, this was definitely a ‘keep calm and carry on’ moment.”