The 40-year-old Somali is the first confirmed coronavirus case at the Moria camp, which as of Aug. 31 housed 12,714 people, several times its capacity of 2,757.
The ministry said no entry or exit from the camp would be allowed until Sept. 15 and that the police presence would be increased around the camp to fully enforce the lockdown.
Only essential staff will be allowed to enter the camp after undergoing temperature checks.
Health authorities said the Somali man’s contacts were being traced and all would be quarantined, while extensive coronavirus tests were being conducted on the camp’s residents.
More than 27,000 migrants and asylum-seekers live in camps on the Greek islands, after arriving from the nearby Turkish coast. Moria, by far the largest of the camps, previously had been free of confirmed COVID-19 cases.
The International Rescue Committee aid group called for vulnerable people to be evacuated from Moria.
Greece has been seeing a spike in coronavirus infections in recent weeks, which authorities have attributed to people on holiday ignoring protective measures such as maintaining social distance. The country was initially credited with tackling the pandemic's initial outbreak well, with an early lockdown keeping the number of seriously ill people and of deaths low.