William Burdett-Coutts, founder of the Assembly Rooms venue, said the “bedrock” of the festival could be destroyed unless its international flavour is preserved.
He warned that the Fringe, which was first staged in the aftermath of the Second Word War, faces being diminished and becoming more inward-looking as the UK comes out of the European Union.
He raised concerns over festival workers, performers and companies being put off coming to Edinburgh by the “tone” of the debate on Britain’s withdrawal from the EU.
And he said there was huge uncertainty over how much red tape artists would face under new immigration and visa rules.
Mr Burdett-Coutts, who has been staging shows at the Fringe for nearly 40 years said Brexit was one of the biggest challenges for the Fringe to emerge in modern times.
He added: “The whole tone of Brexit is making people think twice about coming to this country, certainly for work, and I get concerned about how that will impact on cultural events. The whole move to coming out of Europe is about making it more difficult for people to come here.
“At the moment it is fairly easy for companies to come into the country, but that may change. We’ve done such a good job in attracting people to Edinburgh - the last thing we want to do is put them off.
“The strength of the festival is the number of different people from around the world who come here. Continuing that is the key bedrock of the Fringe. International shows used to be a rarity, but now there is a huge amount of international work.
“We need to get public bodies to stand up and support the Fringe, say how important it is that people keep coming and also making sure that the status of the festival doesn’t change. Symbolically, Brexit is one of the biggest issues facing the festival. If it became more inward-looking it would destroy its ethos, which is about goodwill between nations.”
Speaking at a major tourism and culture summit in Edinburgh, Scottish culture secretary Fiona Hyslop admitted Brexit could have a “devastating” impact over the next few years.
She added: “The challenges we face as we move towards leaving the European Union will mean that being accessible and visible as a tourism destination have never been more important.
“We have seen some benefits to our industry with the weakening of the pound, but we cannot build a strategy based on weaknesses. In Scotland, around 10 per cent of those employed in the tourism sector come from the EU. The potential impact of any future reduction in freedom of movement could be devastating. The same applies to potential barriers such as visa restrictions.
“Europe and the world must know our tourism industry is open for business, that people are welcome in Scotland, and that welcome remains as warm as it ever was.”
Julia Amour, direcor of Festivals Edinburgh, which leads efforts to promote the city’s flagship events around the world, said: “We felt a great wave of support last year from our international partners for the festivals as one of the most international assets that Scotland and the UK has and the importance of making even more of that as the UK leaves the EU.
“There is a sense of threat and risk and making sure that Brexit doesn’t put us in a worse position.
“We have an international partnerships programme and we’re reaching out more than ever with this being the 70th anniversary year to invite international delegations to Edinburgh to make sure that those European links are strengthened.
“We’re very much continuing to develop that internationalist outlook and talking to the policy-makers about freedom of movement and making sure that the festivals continue to thrive.”