It happened on the 20:50 train on Saturday, after Tyrone beat Armagh in the All-Ireland SFC quarter-finals at Croke Park in Dublin.
Gardaí (Irish police) were called and boarded the train at Drogheda at about 22:20 local time. No arrests were made.
Translink said some passengers were involved in "an affray on board".
There have also been some complaints about overcrowding on the train, but Translink rejected complaints that any of its services were dangerously overcrowded.
While the trains were "very busy", they operated within safety limits, said Translink.
Irish Rail staff contacted gardaí at Drogheda Garda Station to inform them of the disturbance on the Belfast-bound train.
Gardaí said they boarded the train, spoke to a number of passengers and calmed the situation down.
"No complaints were made and no arrests took place," added the Garda spokesperson.
"The train departed a short time later without further incident."
Translink said the police were called after a train manager raised concerns.
"A number of passengers were removed (at Drogheda) and the gardaí continued to travel on the train to Dundalk," said a Translink spokesperson.
As a result, the train arrived in Belfast at 00:40 on Sunday - 98 minutes late.
"We would like to apologise to passengers for this delay," said Translink.
Three other extra trains travelled from Dublin to Belfast on Saturday without incident, according to the company.
"Passengers who had reserved a seat on the 8.50pm Enterprise train, but travelled on one of the alternative trains, will be entitled to compensation," it added.
"Translink has a policy that only alcohol purchased on board the Enterprise train can be consumed on the train and we are currently reviewing the implementation of this policy on busy days like this."
In a statement, the Ulster GAA highlighted that the onboard fracas had resulted in no arrests.
"There were 80,000 people at Croke Park on Saturday who travelled, sat together at the game, and enjoyed each other's company," said a GAA spokesperson.
"For some individuals to misbehave, it is difficult to legislate for that."
Clashes between Tyrone and Armagh GAA (Gaelic Athletic Association) fans on the Dublin-to-Belfast Enterprise train are being investigated by Translink.