Officers found an explosive device, thought to be a "flashbang" grenade, when they were called to Elgin Street, Leith, at 12:50.
Police are treating the death of the 51-year-old woman as unexplained and have launched an investigation.
A spokesman said the device was made safe but a controlled explosion was not required.
He said: "Inquiries into the death are ongoing.
"The death is currently being treated as unexplained but the circumstances are not thought to be suspicious.
"A report will be submitted to the procurator fiscal."
A bomb disposal team was called out after a woman was found dead at a house in Edinburgh.