Khublai Khan's in Assembly Street, Leith, has come under fire for selling the shark meat as part of its Mongolian feast.
Advocates for Animals wrote to the restaurant last year after it emerged that they had started serving zebra among their other exotic meats.
The restaurant, which also offers Li Mak - shark and prawn puffs with a lemon and chilli mayo - as a starter, is known for its selection of exotic meats, including kangaroo, yak, ostrich and springbok.
But most worrying for animal rights groups is the inclusion of shark on the menu, with many species already close to extinction from over-fishing.
At present it is thought that more than 100 million sharks are taken from the seas each year, and demand for shark meat is booming, with supermarkets in Europe, South America and the USA now stocking the meat.
Last year alone, UK fishermen landed 760 tonnes of shark with a market value of 631,000. In the same year the UK imported an additional 2530 tonnes, equivalent to approximately 632 lorries of the meat, worth more than 3,532,000.
Ross Minett, director of Advocates for Animals, said: "We were very disappointed to hear that Khublai Khan's had jumped on the exotic meat bandwagon and had chosen to sell shark meat.
"Virtually every species of shark population is in decline.
Restaurants like Khublai Khan's should be ensuring their meats are sourced ethically but they think they can sell shark meat to unsuspecting customers.
"We would urge conservation-conscious people not to eat at Khublai Khan's until they have taken shark meat off the menu."
The sharks are being caught and killed faster than they can breed. It is estimated that by 2017 nearly 20 species of shark will be extinct. The trend is thought to be linked to the decline of other fish species, coupled with a drive to get more people to eat fish as a healthy alternative to meat.
The Food Standards Agency has advised against giving children shark meat.
And worldwide concern is growing over the threat to the animals. Last year a restaurant in the top Egyptian resort of Sharm El Sheikh removed shark from its menu after protests by divers and conservationists led to major companies such as Nestl, Coca Cola and Heineken withdrawing support for the restaurant.
Ali Hood, director of conservation with the UK Shark Trust, said: "The legislation protecting sharks in EU waters is pitiful, and pretty much every species is 'legitimate', even though numbers are declining rapidly.
"Sharks do not have a life-cycle that can sustain heavy fishing, because they breed slowly, live for a long time and mature late, so it takes them a long time to replenish their population. People can make a difference by voting with their feet and if we can reduce or halt demand for shark meat, then it will do some good."
An employee of the restaurant, who asked not to be named, said that the shark meat they used was provided by a reputable Scottish frozen foods wholesale company and stressed that it was not illegal to sell shark in the UK.
He said: "We have had this on offer for over ten years and it is widely available in Britain. If this group really want to do something about it perhaps they should speak to the company that sells it to us." The restaurant owner, Andrew McRobbie, was unavailable for comment as he is currently out of the country.