The migrants were believed to have recently entered the country when the crash happened, according to police.
It comes after a number of migrants who recently crossed from the breakaway north to the internationally recognised south of Cyprus tested positive to COVID-19.
Migrants normally make up the bulk of fruit pickers in Finland, but in this pandemic year, farmers are instead turning to locals for help.
Officials say the two who tested positive did not display symptoms of COVID-19. Other migrants in the facility and people who come in contact with them are being tested.