Around 1am on Thursday, officers were called to a report of a disturbance at a property in Restalrig Avenue.
Emergency services attended and the woman was taken to hospital where she died a short time later.
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A 55-year-old man has been arrested in connection with the assault and enquiries are ongoing.
Restalrig Avenue remains closed while enquiries are carried out.
Detective inspector Kevin Tait said: “Our thoughts are with the family and friends of the woman at this extremely difficult time.
“There will be a continued police presence in the area while our investigations continue and I would urge anyone with any concerns, or information, to approach these officers.”