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."

The 48-year-old singer and actor Joshua Sasse, 28, announced their engagement earlier this year.
The couple subsequently vowed to postpone their nuptials until same-sex marriage becomes legal in Australia.
Dressed in "Say I Do Down Under" T-shirts at the Arias in Sydney, the pair urged the change to come next year.
"We're here to introduce a shining light in the Australian music industry," Minogue told the audience on Wednesday night.
"But we're also here to say thank you to everyone who has supported Josh's campaign for equality."
Sasse, who founded the "Say I Do Down Under" campaign, said: "This is more than a movement, this is people's lives and we want to say to every single member of the LGBT community that you are not alone.
"You have a voice and if we all stand together we can bring Australia back on the right side of history and make 2017 the year that we can all say 'I do' down under."
Australian pop star Sia also used the awards night to address the issue, sending a same-sex marriage campaigner to collect her award for best female artist.
The Australian government's plan to settle the same-sex marriage debate through a public vote early next year was blocked by the Senate two weeks ago.
Critics said a nationwide campaign would be expensive, unnecessary and unleash a torrent of homophobic rhetoric.
Sasse's "Say I Do Down Under" campaign, along with other lobby groups, is now pushing for parliament to change the law.
His campaign has attracted celebrity supporters including Chris Martin, Ellie Goulding and Sir Ian McKellen.

In a post on the social media site, he said his personal challenge this year would be to build a "simple AI" similar to the butler Jarvis from the film Iron Man.
Mr Zuckerberg plans to share his progress over the course of the year.
Last month, he made headlines for plans to give away 99% of his Facebook stake.
He had to defend his philanthropic venture - launched to celebrate the birth of his daughter- after critics argued that it could provide a way for the founder to avoid paying tax on the sale of his shares.
On Monday, Mr Zuckerberg said he would start to build the AI with technology that is already out there and teach it to understand his voice to control everything in his home from music and lights to temperature.
"This should be a fun intellectual challenge to code this for myself," Mr Zuckerberg said.
"I'll teach it to let friends in by looking at their faces when they ring the doorbell," he said. "I'll teach it to let me know if anything is going on in Max's (his daughter's) room that I need to check on when I'm not with her."
It is now a long time ago, but I've been trying to remember my two periods of paternity leave.
I dimly recall clumsily changing nappies, making endless cups of tea for visitors, and a mixture of immense joy and total weariness. What I'm sure I did not do is come up with a plan for a personal robot assistant.
Read Rory's full analysis here.
For Facebook, he added that the system would help him visualise data in virtual reality and help him build better services, as well as lead his company.
His announcement comes as Facebook is in the midst of AI initiatives such as building an assistant through its Messenger app for users.
The tech billionaire said a part of the motivation behind this year's challenge was the reward of building things yourself.
His previous personal challenges have included learning Mandarin, reading two books a month and meeting a new person every day, he said.
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A bomb disposal team was called out after a woman was found dead at a house in Edinburgh.
[NEXT_CONCEPT]
Kylie Minogue and her British fiancÃ© have called on Australia to legalise same-sex marriage in an appearance at the nation's top music awards.
[NEXT_CONCEPT]
Facebook founder Mark Zuckerberg has said he plans to build artificial intelligence (AI) to help him around the house and with his work.