Police were called to the City winger's home in Lower Withington, Cheshire, in the early hours of Saturday.
Sinclair was then questioned before being released on bail, and he has been ordered to report back to police on 25 August.
It is believed the arrest followed an alleged row between the former England man, 31, and wife Natalie at a party. Sinclair lives with his wife and two children.
The club said it was not their policy to discuss the private lives of players.