The case - Scotland's first for 10 years - was discovered following the death of an animal. Tests are now underway to determine the source of the disease.
Fergus Ewing, Scotland's farming minister, confirmed that the Scottish government was responding to the incident and had quarantined the area.
However, he went on to calm fears that the disease may have entered the food chain, and stated: "a confirmed case of classical BSE does not represent a threat to human health".
He added: "There is no risk to consumer health as high levels of consumer protection are already in place. These include controls on animal feed and removal of the parts of cattle most likely to carry BSE infectivity.
"Consumers can be reassured that these important protection measures remain in place. No meat from the affected animal has entered the food chain."
Bovine spongiform encephalopathy caused serious harm to the British beef industry across the 1990s and 2000s, and resulted in a block on exports of the meat to the EU for a decade. During the peak of the outbreak in 1993, 1,000 new cases were reported every week.
Ian McWatt, director of operations at Food Standards Scotland, also worked to allay concerns, saying that there are procedures to protect the food chain.
He said: "There are strict controls in place to protect consumers from the risk of BSE, including controls on animal feed and removal of the parts of cattle most likely to carry BSE infectivity.
"Consumers can be reassured that these important protection measures remain in place and that Food Standards Scotland official veterinarians and meat hygiene inspectors working in all abattoirs in Scotland will continue to ensure that in respect of BSE controls, the safety of consumers remains a priority."
Chief veterinary officer Sheila Voas added: "While it is too early to tell where the disease came from, in this case its detection is proof that our surveillance system is doing its job.
"We are working closely with the Animal and Plant Health Agency to answer this question, and in the meantime, I would urge any farmer who has concerns to immediately seek veterinary advice."