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.
A murder inquiry has begun after a woman was found with fatal stab wounds at a house in Greater Manchester.