A 40-year-old woman has been diagnosed with coronavirus in Lesbos, doctors said Monday, in the first reported case on the Greek island.

Greek authorities have expressed concern over the possibility of the virus spreading on islands such as Lesbos, where thousands of migrants are crammed in overcrowded camps or living rough.

The woman recently travelled to Israel and Egypt and was placed in quarantine on Sunday, the public ERT television reported.

More than 1,700 asylum seekers arrived in Greek islands on the Aegean sea last week, the majority in Lesbos, after Turkey decided to open its borders with Greece to pressure the European Union to implement what it says are unfulfilled pledges under a previous migrant deal.

In Lesbos, more than 19,000 asylum seekers have been sheltering in a reception centre at Moria, built to hold about 3,000 people.

Greece's health ministry on Monday reported 11 new coronavirus cases but did not mention Lesbos.

AAP

A total of 84 cases have been reported in the country.

Greece has banned public gatherings, closed several schools and universities and ordered professional sports events to be held behind closed doors for 15 days beginning Monday.