Laura Marshall, 31, was found dead at an apartment block on Victoria Street in Lurgan on Sunday night.
A 36-year-old man has been arrested in connection with the death and is being questioned by police.
The police initially said Ms Marshall’s death was being treated as suspicious.
But following the results of a post mortem examination, detectives started a murder inquiry.
The officer leading the investigation, Detective Chief Inspector Eamonn Corrigan from Serious Crime Branch said: “Laura’s body was discovered at approximately 5.30pm yesterday, Sunday, 3 April.
“I would appeal to anyone who may have seen or had any contact with Laura over the weekend to contact Detectives at Mahon Road on 101 or alternatively information can be passed anonymously to Crimestoppers on 0800 555 111.
“I also want to hear from anyone who saw or heard any activity at Laura’s home in Victoria Street over the weekend until yesterday evening at 5.30pm.
Local DUP councillor Carla Lockhart said the news was ‘devastating”.
“Victoria Street is a close knit community and people will be devastated with the news.”
SDLP MLA Dolores Kelly she Ms Marshall was “very popular and outgoing”.
“There is a great deal of shock and sadness,” Ms Kelly said.
“She was loved by many and it is such a brutal end to such a beautiful young life.”