The case of so-called mad cow disease, known in full as Bovine Spongiform Encephalopathy, was identified at the unnamed farm in Aberdeenshire as part of the routine testing of all fallen stock over four years of age.
A movement ban has been put in place at the farm as investigators try to establish the source of the fatal disease.
Scotland’s chief vet Sheila Voas said up to four other cows on the farm will be slaughtered and tested for the disease.
Speaking on BBC Scotland’s Good Morning Scotland radio programme, she said: “The animal itself is dead, she died before she was tested, and there are three other animals, or possibly four, that will need to be slaughtered purely from a precautionary basis.”
She said brain stem samples would be taken from these animals and tested for BSE.
She believes the disease was not transmitted and occurred spontaneously in the affected animal, but she warned it could be several months before investigators could say for certain.
“All the information we have is this is under control, there’s no reason for people to panic,” she added.
“It’s not the start of an outbreak, it’s a single isolated case that won’t affect the food chain.”
Officials have stressed the case poses no risk to human health and its discovery proves the surveillance system in place is working effectively.
However, any farmer with concerns is advised to seek immediate veterinary advice.
Millions of cattle were culled in the UK in the 1990s during a BSE epidemic.
It can be passed on to humans in the food chain, causing a fatal condition called variant Creutzfeldt-Jakob disease (vCJD).
Strict controls were introduced to protect consumers after the link was established in 1996.
The disease has been reduced to a handful of cases each year in the UK, with the last recorded case in Wales in 2015.