Chief Medical Officer Dr. John Lee reported on Monday that of the 455 COVID-19 tests carried out since Friday, two were positive.
The individuals who tested positive are travellers who arrived on flights last month. Both are asymptomatic and will remain in isolation until they return negative results.
As of Monday evening, the total number of people in isolation, either at a government facility or in their homes, was 647.
Cayman currently has nine active cases of coronavirus. Of those, one case is symptomatic and that person remains hospitalised, officials said.
Since testing began in March, 242 cases of COVID-19 have been detected. A total of 47,377 tests have been carried out.
Worldwide, more than 45.9 million cases have been confirmed.