Two of the officers were taken to hospital after a mob forced its way through the back gates and tried to kick a door down.
Police used batons and dogs to push the protesters, who had scarves covering their faces, out of the courtyard at the back of City Hall on to the street.
The officers were injured after a firework, bricks, bottles and other missiles were thrown.
It is believed a security guard was also hurt. Cars belonging to councillors and staff were damaged.
Sinn Fein's Jim McVeigh said: "The people that broke through the gates are a bunch of thugs. We won't be intimidated by those people."
Councillors agreed by 29 votes to 21 to bring City Hall into line with Stormont and other Government buildings and fly the flag only on 17 designated days.
It is the first time the Union flag has been taken down from the Edwardian building in more than a century.
Ulster Unionist Jim Rodgers said: "I cannot condone violence but people do not realise how strongly the people in Northern Ireland think about flying the flag over City Hall."
Maire Hendron from the Alliance Party said the violence was orchestrated through social media. She added: "Tonight was a disaster for this city."