Kerrie King, who was just 33, died suddenly in a house at Carrickdale Gardens, just off the Tandragee Road.
The PSNI said they were treating the death of the mother of one as ‘suspicious’.
A man in his 50s has been arrested and taken to Musgrave Custody Suite in Belfast.
Kerrie, who was originally from Dundee in Scotland, had been living in Belfast.
Flowers have been left outside the house were she died.
On Tuesday a PSNI spokesperson said: “Detectives are investigating the circumstances surrounding the sudden death of a woman in Portadown reported during the early hours of this morning (Tuesday, February 9th).
“A post mortem examination will take place in due course to determine the cause of death.
“A 50-year-old man has been arrested as part of the investigation and has been taken to Musgrave Custody Suite.
“There are no further details at this time.”
Upper Bann DUP MLA Jonathan Buckley said: “I understand that a 50-year-old man is in police custody following the sudden death of a woman in Portadown that took place in the early hours of Tuesday morning.
“First and foremost, my thoughts are with all the family and friends of the deceased at this time.
"This is a tragic and shocking incident for the area and I would implore anyone who may have information to come forward to the police.”
The Policing Board member has urged anyone with information to come forward to police.