The Three Birds Restaurant in the capital came up with the idea during a revamp of its selection of ice creams.
Owners Kath Byrnes and Jo Curtis say news of their creation went viral prompting an online frenzy.
Since going on the menu last month, diners from New Zealand, the USA and Canada have visited the Bruntsfield eating spot to try the salty and sweet dish.
Miss Curtiss said: “We’ve had people from all over the world seeking us out after seeing a post about our Marmite ice cream on Facebook.
“People either love it or hate it – Marmite is just that kind of food.”