The woman was detained in the Omagh area on Wednesday 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.
Five people have appeared in court charged with affray in relation to the murder. They were bailed on strict conditions and are due to return to court on 22 January.