The 43-year-old woman died at the scene and a 17-year-old girl and a 64-year-old man were in hospital with life-threatening injuries, police said.
Greater Manchester police said a 22-year-old man had been arrested and the “early indications” were that he was known to the victims. The force said the stabbing in the Gorton area of east Manchester was being treated as an isolated incident.
Armed officers were among those sent to an address on Barnard Road at about 11.20pm on Sunday, police said.
Three forensic tents were in place on Monday morning – one outside a property, another in the front garden, and a third in the road.
Man arrested on suspicion of murder after woman fatally wounded and two other people badly injured in Gorton.
Det Supt Toby Facey said: “We understand that the local community and further afield across Greater Manchester will be rightly shocked and concerned after waking up and hearing this tragic news this morning. Our thoughts remain with those affected and their loved ones at this difficult time.
We are doing all we can to support them.
“Within minutes of the call being made, our officers were at the scene and an arrest had been made. An investigation has been launched and we are in the very early stages of our enquiries.
We have had detectives on the ground who have been working throughout the night trying to get to the bottom of what has happened and why.”
He appealed for members of the public to come forward with any information about the incident by contacting police on 101.