The woman stabbed to death in a Dungannon street has been named locally as Luisa Silva Perriera.
A man was taken to hospital with serious knife wounds. Both Ms Perriera and the injured man are believed to be migrant workers.
The incident happened in the Merron Mews area on Thursday afternoon.
It is understood Ms Perriera was in her 20s and originally from East Timor.
It is believed she was a mother-of-two.
A number of local people witnessed what happened. It is believed to be a domestic incident.
One eyewitness said: "My mum came into my room and happened to look out of the window. I looked out when she asked me what was going on and just saw the two of them lying there.
"We went outside and shouted for someone to ring an ambulance but one of the neighbours had already done it."
DUP MLA, Lord Morrow, said people in the area had witnessed an "horrific incident".
He added: "The schools are off at the moment, children are playing, young fellas are kicking football as would happen in in any normal community and that was happening here."
Police have appealed for anyone who was in the area on Thursday afternoon and has information to get in touch with detectives in Dungannon.