The sportsman, who became a father for the first time in May, is suspected of injuring two 19-year-old men.
According to Greater Manchester Police, the teenagers were assaulted on Russell Street before 1:30am on 4 July.
A police spokesman added that the injuries were not serious and that 27-year-old Amir had been questioned over the incident.
Amir Khan and wife Faryal welcome baby girl
WBA and IBF light welterweight champion Amir has been released on bail until mid July. The Olympic sliver medallist has yet to comment on the arrest but his management company, Tangerine PR, released a brief statement.
"Amir Khan was arrested on suspicion of common assault in the early hours of Friday July 4. Amir has since been released without charge on bail pending further enquiries. At the stage we are unable to comment further on this matter."