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."
More than 13,000 email addresses have been stolen from Edinburgh city council's database following a "malicious cyber attack".