Patrycja Wyrebek (20) was found dead at her home in Drumalane Park, Newry, on Sunday morning.
A 23-year-old man has been arrested and on Monday afternoon.
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Detective Inspector Mark Gibson has made an appeal for information to help in the investigation.
“My thoughts are very much with Patrycja’s family and friends at this extremely sad time,” he said.
“I would appeal to anyone who was in the Drumalane Park area of Newry between 8.30pm on Saturday, August 1st and 8.30am on Sunday, August 2nd and who saw or heard anything suspicious to contact detectives on the non-emergency number 101, quoting reference 692 03/08/20.”
