The attack happened in the Castleblaney Street area of Newtownhamilton.
Detective Inspector Leah Crothers said: “We received the report yesterday afternoon, just after 2 pm, that a female had been assaulted by a male in a house in the Castleblaney Street area.
“She subsequently ran from the house and, in a distressed state, was comforted by local people who contacted police.
“A 38-year-old man has since been arrested on suspicion of rape and threats to kill.
“He remains in police custody, assisting with enquiries.
“Our enquiries are continuing and we are appealing to anyone with information to contact us on 101, quoting reference number 945 of 15/08/19.
“We would like to thank the local community who came to the aid of the victim.”