The breach happened 10 days ago when the council's website service provider, which is based in England, was targeted by hackers.
The City of Edinburgh Council assured those affected no other personal details were accessed.
Officials have warned of a potential increase in spam or phishing emails.
They said the incident had been reported to both the Information Commissioner and the UK Government's Computer Emergency Response Team and that extra security measures had been put in place.
A council spokeswoman said: "This was a malicious cyber attack on the council's website which is hosted in a UK data centre. It was dealt with swiftly and at no point were any council services affected.
"We are contacting everyone who has been affected to inform them of the incident and offer them advice and support. We have reassured individuals that the only details that have been accessed are their email addresses.
"The Information Commissioner's Office has been informed and preventative measures have been taken by the web service providers.
"We want to reassure the public the ongoing security of our website is critically important, and we continue to work with our service providers to ensure that the risks associated with attacks are dealt with."

Joel Andresier, 39, from Southampton, said the pushchair had been covered in "pretty much every bodily fluid known to science" by his three children.
At one stage the highest bid for the three-wheeler stood at more than £150,000, after the advert went viral.
He reset the price after admitting he did not expect the bidder to pay up.
In the listing's description, Mr Andresier, of Sarisbury Green, said: "This was purchased against my wishes many years ago as I never wanted any children and a buggy signified my wife's intent to have children.
"We argued much and this buggy signifies everything that ended my happy carefree low cost child free life."
It prompted six pages of questions which led the advert to exceed the number of customer enquiries allowed by the online auction site.
Mr Andresier wrote: "Looks like I have hit the eBay limit for shared responses to all your wonderful questions. It doesn't look like the last 50 or so replies from today have been added to the listing. Sorry people - looks like you have broken eBay."
On the comments pages, one user described Mr Andresier as a "marketing genius", while another did not see the funny side and said he was "pathetic".
He said he would use the proceeds from the sale to "help me recover from children".
Mr Andresier's wife Susan, 36, had said she found the listing "hilarious", and added the couple had been amazed by its popularity on social media.
'Green monster' for sale: Highlights from the eBay listing
"I have bought cars that cost less than this buggy. My dad once bought a house that cost less than this buggy.
"Anyway as you can tell I hate the buggy. I now have 3 children, and a Labrador and am forced to endure the school run where women I dont know try and discuss the price of centre parc holidays, and the benefits of the micro over the mini micro scooter. To summarize my life is over and this green albatross needs to go round some other poor sods neck.
"All of my children are now walking (often in completely the wrong direction) but someone else deserves to give this a good home. Over the years I have collected spare bits from other zombified fathers who were once full of life and I will throw these in as well."

The 29-year-old's body was discovered at the DoubleTree by Hilton on Eastfield Road on Saturday at about 19:25.
Emergency services were called but the man was pronounced dead at the scene.
A Police Scotland spokeswoman said: "Inquiries are currently ongoing, however the death is not being treated as suspicious."
A report will be sent to the procurator fiscal.
More than 13,000 email addresses have been stolen from Edinburgh city council's database following a "malicious cyber attack".
[NEXT_CONCEPT]
A used buggy listed for sale by a father who joked that it signified the end of his "happy carefree life" has sold for £325.
[NEXT_CONCEPT]
A man has been found dead in the swimming pool of a hotel near Edinburgh Airport.