The man was detained in the Omagh area on Monday afternoon and is assisting police with their enquiries.
Jason McGovern had been socialising in Omagh on the night of Sunday, 30 December. In the early hours of the following morning, New Year's Eve, he was assaulted twice.
The 19-year-old, who was from Co Monaghan, was first attacked at the Terrace Bar on John Street after an altercation with a large group of people at around 2am.
Mr McGovern then went to the nearby Kelvin Road, close to the Weigh Inn bar, where he was approached again. The victim was punched in the face and fell backwards onto the ground.
After falling unconscious following the second attack, the young man was helped into a taxi and taken to his friend's house at Emyvale, Co Monaghan.
He was found dead in bed last Monday at around noon.
To date, four young men and one youth have been charged with affray in relation to the death.
It's very very tragic that his death would come in the manner that it came and at a time of the year when people would be looking forward to the New Year and new beginnings.
Brian McKenna, SF Monaghan Councillor
The latest arrest follows an appeal from PSNI a week on from the murder.
They released a photograph of the victim, which was taken on the night he was assaulted.
The officer leading the investigation, Detective Chief Inspector Richard Harkness, said: "There were a large number of people socialising in the area at the time of the assault and also a number of motorists in the area of John Street and Kevlin Road.
"I have a specific appeal to any pedestrians or motorists who were in the area of the Terrace Bar or Sally O'Brien's nightclub in John Street Omagh at approximately 1.55am and witnessed the assault on Mr McGovern and his friend, or a short time later at the Weigh Inn car park at Kevlin Road and witnessed Mr McGovern being assaulted for a second time to come forward and speak to police if they have not already done so."
DCI Harkness said that while officers had made a number of arrests, this investigation will continue for some time.
He continued, adding "we are asking for people's assistance about information surrounding the events that led to Jason's death."
"We are grateful to people who have co-operated with our enquiries in the past week. The assistance of local people will be vital if we are going to bring those responsible for Jason's murder before the courts."
Sinn Féin Monaghan Councillor Brian McKenna says many people from the surrounding area have been in touch to express their sympathy and that both communities are still in shock.
"From my own colleagues in council in Omagh, there is absolute shock with them that this incident happened in their town," he explained.
"He seemed to be by all reports, a very quiet, well-mannered young man, who looked after his granny, who looked after his mother who is in a wheelchair with MS."
Anyone with any information can contact detectives in Omagh on 0845 600 8000.
Mr McGovern's funeral took place on Monday at St Patrick's Church in Corracrin, Co Monaghan.