The body of the 46-year-old was discovered in the property in Loudoun Road, Newmilns, East Ayrshire, at around 11.10pm yesterday.
A post mortem is to be carried out to determine exactly how the woman died, but police are treating it as suspicious.
Officers remain at the scene of the death and are said to be following a definite line of inquiry.
A force spokeswoman said: "Around 11.10pm last night the body of a 46-year-old woman was found within a flat in Loundoun Road, Newmilns.
"A post mortem is due to take place to establish the exact cause of death, however at this time we are treating it as suspicious and inquiries are continuing."