The 39-year-old died at the scene shortly after police had arrived at the house in Cheadle Road, Cheadle Hulme, at about 19:40 BST on Monday.
A man, 39, was later arrested on suspicion of murder and Greater Manchester Police said they were not looking for anyone else.
"Our thoughts go out to the family of the woman," Det Supt Tony Creely said.
He appealed for witnesses or anyone with "information which could help us with our investigation" to contact police.
"The investigation is in its very early stages, however, we are not looking for anyone else in connection with the murder," Det Supt Creely added.

Gladstone's Library in Hawarden said it had not been asked for permission.
Warden Peter Francis said it gave the impression the library was "supportive of UKIP and its policies".
UKIP has not apologised and claimed the party was "closest ideologically" to the Liberal Party Gladstone joined.
Formerly known as St Deiniol's Library, it was founded by the former prime minister whose home and estate were nearby, being renamed in his honour in 2010.
The UKIP manifesto for May's assembly election, launched in Newport on Friday, includes a photo on the page outlining local government policy.
"The policies and principles on which UKIP is based are far from the ideals of William Gladstone," Mr Francis said.
"Gladstone was an internationalist and profoundly believed that the 'sanctity of life in the hill villages of Afghanistan among the winter snows are as inviolable in the eye of Almighty God as can be your own'.
"That is to say he felt that the unity of human beings throughout the world was vitally important and 'not limited by the shores of this island.''
Mr Francis added the library "would like to reiterate that it supports no political party but upholds 'liberal values' wherever it sees them.
"To imply Gladstone's support for their cause, as this UKIP photo clearly does, is to devalue the memory and legacy of William Gladstone."
UKIP candidate Mark Reckless said the photo had been taken from the public highway by a photographer who had given the party permission to use it.
A spokesman added: "UKIP is a party founded on the principles of liberty and in particular self-governance and the protection of personal freedoms and is closest ideologically to the old Liberal Party that Gladstone joined as a Peelite.
"Gladstone was a great orator and believed strongly in holding public meetings, something that UKIP also firmly adheres to, and was a great advocate of preserving the UK's dominion.
"In fact, you would be hard pressed to find a modern day party more closely related to the principles of Gladstonian liberalism than UKIP.
"It's a shame that the people overseeing this great public library do not seem to understand anything about the politics of the great man who founded it."

Bristol-based artist Luke Jerram created the work called Maya using more than 5,000 photographs of his daughter.
Mr Jerram said he was inspired by the "billions of images uploaded to the internet every year".
The piece has been installed on platform three, where Mr Jerram's daughter saw it for the first time.
'Coloured stickers'
Mr Jerram, who is the artist behind Play Me I'm Yours, which has seen pianos appear on city streets around the world, said: "From a distance, people coming through the station may be almost concerned to see what looks like a young girl stood by herself, but as they move closer, she will pixelate just like a computer image does.
"There's a certain distance when standing in front of the sculpture that the pixels disappear and the image of the girl comes together.
"The sculpture goes ping - it's really fun."
The artwork was made by scanning Mr Jerram's daughter using an Xbox Kinect.
Her head was scanned at the Machine Vision Laboratory at the University of the West of England where Mr Jerram is a visiting Senior Research Fellow.
Both scans were then combined and pixelated into cubes, called voxels.
The model was then made from precision-cut sheets of aluminium.
Finally more than 5,000 coloured stickers were printed and fixed on to the aluminium.
The sculpture is part of a series of Bristol Temple Quarter Commissions, designed to engage people with the new Temple Quarter Enterprise Zone.
The aim is to encourage artists and audiences to explore the area, engage with its history and its future.
A murder inquiry has begun after a woman was found with fatal stab wounds at a house in Greater Manchester.
[NEXT_CONCEPT]
A Flintshire library dedicated to 19th Century Liberal Prime Minister William Gladstone has complained to UKIP after the party used a photo of it in its Welsh manifesto.
[NEXT_CONCEPT]
A sculpture of a girl which appears to fragment as the person looking at it moves closer has been installed at Temple Meads railway station.