A number of police officers were injured when bottles, masonry and other missiles were thrown in the West Street area of the town on Wednesday night.
Riot police fired a number of baton rounds as they dealt with the disorder, which started after 7.30pm. Two men and two women have been arrested.
"Crowds have dispersed in Carrick town centre; however police are maintaining a presence in the area", a PSNI spokeswoman said.
UTV's Sharon O'Neill tweeted from the scene: "The situation appears to have been brought under control."
The trouble erupted in the wake of a council vote restricting the flying of the Union flag at Belfast City Hall earlier this week.
Up to 1,600 people taking part in a loyalist protest gathered in the Irish Gate roundabout area on Wednesday evening - the majority of the crowd later dispersed before trouble broke out.
The constituency office of Alliance East Antrim MLA Stewart Dickson was set alight during the disturbance, causing smoke damage.
This campaign of intimidation against the Alliance Party cannot be allowed to continue.
Other premises in the West Street area were entered during the disorder and windows were smashed.
"The premises were ransacked with substantial damage caused," police said.
Mr Dickson said graffiti was sprayed across his constituency office on Tuesday night.
He said: "This is an outright attack on democracy and cannot be allowed to continue."
"The Alliance Party will not continue to be bullied and intimidated by Unionists," he added.
Leader David Ford previously said the party would not be intimidated after one of his councillors had to leave her Belfast home this week due to a security risk.
The Alliance Party has requested that the Assembly be recalled in light of the violence.
Mr Dickson blamed the DUP and UUP for "whipping up Unionist tensions".
"They must be held accountable for their actions," Mr Dickson said.
I unreservedly condemn the violence. Those involved do a disservice to the flag they claim to defend.
Condemning the trouble, DUP East Antrim MP Sammy Wilson described the scenes in Carrickfergus as "carnage".
"People are entitled to peacefully protest but there is absolutely no justification for the carnage which has been caused in Carrickfergus this evening.
"I urge those involved to step back from this criminal activity and channel their energies through democratic politics," Mr Wilson added.
Ulster Unionist Party leader Mike Nesbitt said violence was "wrong, legally and morally".
"What unionism needs today is brains, not brawn. We need an analysis, a strategy and an agreed outcome," he said.
"I am happy to talk to anyone, if they commit to repent and desist from violence."
SDLP leader Alasdair McDonnell said violence was "unjustifiable".
"Stewart Dickson is doing his best for the people of East Antrim and an attack on him is an attack on everybody in East Antrim," he said.
"The SDLP stands fully with the Alliance Party in utter abhorrence to this attack."
On Monday night 18 people were hurt when violence flared in Belfast following the passing of the Alliance motion. First Minister Peter Robinson described the scenes as "totally unacceptable".
Police in Carrickfergus liased with local community representatives in their effort to restore calm.