Post-mortem testing indicates that the sheep died of the atypical NOR-98 form of the illness, which strikes the central nervous system. The last such case was found in Finland last August.
All of the sheep on the farm, about 200, will be put down to prevent spread of the disease.
Scrapie is classed as a transmissible spongiform encephalopathy (TSE), as is the better-known BSE or 'mad cow disease'. However scrapie is not known to have ever transferred to humans.
There are only some 90,000 sheep in Finland, as compared to 1.4 million pigs and just under a million cattle.