The blaze took place in a ground-floor property at a four-storey block in Edinburgh’s Dundee Terrace on Wednesday evening.
Police said the formal identification of the woman who died has yet to take place.
Two other women suffered burns and a baby girl sustained minor injuries in a separate blaze in the city’s Pilrig area around the same time.
One of the women, aged 26, is in a critical condition. The other, who is aged 59, was stable.
It is understood the Pilrig fire followed an aerosol explosion and is not being treated as suspicious.