The march - which could attract up to 15,000 people - is being planned for Saturday September 13th - just five days before voters will take part in the referendum.
Police have not raised any objection to the march, despite the risk of increased tensions given its proximity to the vote.
And senior councillors have voiced fears that any trouble at the march would be picked up by the world’s media and tarnish Edinburgh’s reputation.
One councillor told the Evening News: “I have really serious concerns about the public order implications of the march.”
A 12-year-old girl was hit by a bottle thrown during a similar march in Glasgow earlier this month after a fight broke out.
Councillors fear that police are underestimating the risks.
The same councillor added: “The Glasgow parade was a march of 4500, so the one proposed for Edinburgh is significantly larger. Feelings will be heightened by the proximity to the referendum.
“The whole world is going to be looking at Edinburgh during that week and it could be a really bad advert for the city if it goes wrong.
“There will be lots of press here and lots of cameras that week. Edinburgh could find itself in the news for all the wrong reasons.”
Councillor Gavin Barrie - who leads the city’s licensing sub-committee, which will have the final say on whether the march goes ahead - said: “We will give due consideration to professional advice and make a balanced decision, taking account of people’s right to march. We have to have an extremely good reason for refusing that.”
The march, which has been advertised as an anti-independence rally, will follow the Commonwealth Games and Edinburgh Festival, and will take place just days before the start of the Ryder Cup at Gleneagles.
Robert McLean, executive officer of the Grand Orange Lodge of Scotland, dismissed fears over the march, adding: “We have paraded through Edinburgh on many occasions without problems.”
Mr McLean claimed that the trouble seen at the march in Glasgow was ‘nothing whatsoever to do with the parade’.
He continued: “This is an all-Scotland march so we have members from all over the country. We had an all-Scotland march in Edinburgh in 2007 with 15,000 to 20,000 people and there were no problems at all.
“There won’t be any trouble from the Orange parade.”