Officers from Greater Manchester Police were called to an address on Richmond Street at around 5 a.m. on Saturday after reports of a disturbance, News.Az reports, citing Sky News.
After arriving at the location, they found a man with a leg injury "consistent with a gunshot wound", according to Greater Manchester Police.
The force said he was taken to hospital but his injuries were not believed to be life-threatening.
A firearm was also recovered at an address in Richmond Street, the force added.
Six men aged between 23 and 26 years have been arrested on suspicion of affray and firearms offences.
They remain in police custody for questioning and investigations are ongoing.
Superintendent Stephen Wiggins said: "This will undoubtedly be a concerning incident to be waking up to, not just for those who live and work in the city centre, but for the whole of Greater Manchester."
Police are appealing for witnesses or people with any information about the incident to contact them.
