"That has been the idea for a long time. So the only thing we ask of our staff is that they have an interest in veganism," Eiriksdóttir said.
However, she also told the publication no specific dietary requirements were needed to work in her restaurant, instead insisting the letter had been worded in a misleading way.
The Reykjavik Grapevine reports that Iceland has been cracking down on workers' rights and discrimination in the workplace in recent years, with gender discrimination at work strictly outlawed.
However, the Gló case is the first to highlight potential discrimination based on dietary choices.
Veganism is a growing trend worldwide and is especially common in the United Kingdom, with the BBC reporting the number of vegans had jumped from 150,000 in 2006 to 542,000 in 2016.
The trend is growing in Australia as well, with the number of Aussies eating a mainly vegetarian diet rising by over 23 per cent in the last four years, according to Roy Morgan research.
Animals Australia has also claimed veganism was the fastest growing food movement in the world.