The Facebook message was posted on a page used by EH4 Residents Association and removed after the group was contacted by the Evening News.
The organisation was set up to represent residents living in Drylaw Crescent, Drylaw Gardens and House O’Hill Road, and works to address concerns over issues such as crime, traffic and street lighting.
Posted on May 30, the message read: “Ramadan is early this year. Jun 18-Jul 17. If you live close to the [Blackhall] mosque and have to stay put, might be an idea to stock up on headphones/ earplugs etc.”
Foysol Choudhury, chairman of the Edinburgh and Lothians Regional Equality Council, said the post would have been seen as offensive to Muslims.
He said: “For anyone to refer to the use of headphones to avoid hearing prayers from a mosque is a hateful religious and racial insult that is based on Islamophobia.
“When a group of people talk about something in that way, it’s going to go to more people. It expresses an undercurrent of hatred. Just giving ideas to people is dangerous.”
He added: “What has been posted is encouraging other people to open up a chapter and start talking negatively. There should be a strong line drawn here – not only for Muslims but for all religions.”
Political figures said they were aware of past concerns over noise and congestion caused by parked cars around Blackhall Mosque.
But they stressed mosque leaders had taken steps to address these, adding that no recent complaints had been received.
Councillor Iain Whyte, Conservative member for Inverleith, said: “I know the mosque has gone out of its way to reduce any noise that comes from the building.
“My understanding is that if somebody feels offended for reasons of race or religion then that is an offence. I would hope that if people have said something that has caused offence, they would recognise that and apologise for it.”
Councillor Lesley Hinds, Labour member for Inverleith, said: “It’s clear [that] people have found this insulting and I welcome the fact that the group has taken account of that and taken [the post] down.”
Police Scotland said it had not received any complaints, but said an assessment would be carried out to see if further investigation was needed.
Ramadan is the ninth month of the Muslim calendar and is observed worldwide as a period of fasting to commemorate the first revelation of the Quran – Islam’s central religious text – to the prophet Muhammad.
The Evening News made repeated attempts to speak to the EH4 group, but no-one responded to our messages.
Leaders at Blackhall Mosque also declined to comment.