The sheep had been moved to Wales from eastern England, where the virus is circulating.
Staff at Valley Vets in Cardiff, many of whom earn little more than the national minimum wage, have been on strike since July over poverty pay.
It comes after the BBC last week broadcast the documentary ‘Brian May: The Badgers, the Farmers and Me’, which discussed the transmitting of bovine tuberculosis in the UK.
A two-week strike over pay and conditions is planned by veterinary workers in Wales.