It declared [in French] employees would be prohibited from leaving military bases throughout the nation in an attempt to contain the illness.
Switzerland has compulsory military service and a high proportion of its military consists of conscripts.
Included in the conscription system, soldiers need to take annual refresher classes, which last a few days.
The soldier examined positive as he started a refresher class on Monday, the Korean Army said in a statement. Throughout tests, he disclosed that he had been to Milan and army chiefs chose to test him.
The military said his condition was stable and the 3 individuals in his area were quarantined. The other soldiers that had been connected with the infected individual were put in temporary quarantine overnight.
Other troops could still leave military buildings, but not the military websites, a Swiss military spokesman told AFP.