A three-kilometre (1.9-mile) protection zone has been set up after two tests carried out by veterinary surgeons on a herd of 300 sheep on a farm near the southern port city of Larnaca had proved positive.
"There's no need to panic. We have taken precautionary measures," Photiou told reporters.
Restrictions have been placed on the movement of an estimated 15,000 animals, including sheep and other livestock, inside the protection zone near the village of Dromolaxia.
Samples have also been sent for analysis to the British EU-accredited laboratory in Weybridge, Surrey, and the results are expected on Wednesday, the minister said.
The last reported outbreak of foot and mouth disease on the island was in 1963.