Two female officers have been hospitalised, although their injuries are not believed to be life-threatening.
Two security staff at City Hall have also been injured, one of whom suffered cuts to his face and head.
A Press Association photographer sustained an injury when he was hit by a police baton.
Sporadic violence also broke out in east Belfast, with reports that St Matthew's Catholic Church on the Newtownards Road came under attack.
A large crowd of loyalists also gathered in the Albertbridge Road area, where a bus was hijacked on Monday night.
"Crowds have now dispersed from the City Hall and Newtownards Road areas," a police statement said.
"Police remain in the Albertbridge Road area while crowds disperse after disorder in that area," the police spokeswoman added.
Over 1,000 people gathered to protest outside City Hall ahead of the council meeting.
Trouble erupted after protesters broke through police lines and tried to gain access to the grounds through the rear gates shortly after the vote.
Windows were smashed and it is believed cars in the vicinity have also been damaged.
"Security inside seemed overwhelmed by the situation", UTV's Sharon O'Neill said.
Officers in riot gear and dogs were brought in to try to bring the situation under control.
The flag has flown outside the historic building every day for more than a century.
The Alliance amendment supporting the flying of the Union flag on 17 designated days was passed by 29 votes to 21.
Party leader David Ford described the result as "a clear victory for the Alliance Party".
The move brings Belfast City Hall into line with Stormont and other Government buildings.
It comes after the council's strategic policy and resources committee voted 11-9 in favour of removing the flag completely last month - a move supported by Sinn Féin and the SDLP.
Unionist politicians did not back the proposals.
Alliance Councillor Laura McNamee condemned the violent scenes at one of Northern Ireland's most iconic buildings.
"We recognise anyone's right to a peaceful protest, however what has been taking place outside Belfast City Hall tonight has been neither peaceful or respectful. This was proven when a number of protesters pushed past police and invaded the City Hall."
Sinn Féin councillor Jim McVeigh said: "Unfortunately it looks like the police were not prepared for the threat.
"The people that called this rabble, these thugs onto the street have to take responsibility and that's some of the politicians at City Hall as well," the councillor claimed.
Mr McVeigh added that the politicians in question should condemn the violence and "go out and reason with these people."
DUP Councillor Alex Easton said that people needed to realise the frustration in the Unionist community over the removal of the Union flag.
He added: "We condemn any violence. It's not something we want to see.
"Nobody wants to see anyone getting hurt. Any person that's hurting anyone is wrong and it has to be condemned."
Ulster Unionist Jim Rodgers said he was not surprised violence had flared.
"There is a real anger," he said. "I cannot condone violence but people do not realise just how strongly the people in Northern Ireland think about flying the flag over City Hall."
SDLP councillor Tim Attwood said the violence was "an outrage."
"This was an appalling spectacle, resulting in significant damage to property and, most alarmingly, injury to a number of those seeking to keep City Hall secure, and our thoughts are with those who were hurt.
"Any attempt at a resort to mob rule cannot be countenanced," he added.
Traffic was disrupted in the city centre and in east Belfast on Monday night.