No further information was immediately available on the previous movements of the 38-year-old woman, though one Greek media outlet, Proto Thema, said she had travelled to Greece by road.
Greece has not introduced any travel restrictions to Italy, which is the country in Europe most affected by the outbreak with more than 370 cases and 12 deaths reported.
“She is in good health and is being monitored by a team of exceptional colleagues in Thessaloniki,” health ministry representative Sotiris Tsiodras told a news briefing.
Authorities are in the process of identifying people the woman has come into contact with, he said, adding that those who have been in close proximity would be placed in isolation.
A health ministry official said 10-15 people the patient had been in touch with had already been quarantined.
Coronavirus is believed to have originated in a market selling wildlife in the Chinese city of Wuhan late last year and has infected about 80,000 people and killed more than 2,700, the vast majority in China.
It causes respiratory symptoms similar to a cold or flu and like other respiratory infections, it spreads between people in droplets from coughs and sneezes.
Authorities in Athens unveiled a contingency plan on Tuesday which includes school closures, bans on public gatherings and suspension of all means of public transport in the event of a health emergency.
“The first case of coronavirus has been confirmed in our country. It was something we expected and we are absolutely prepared,” said Vassilis Kikilias, Greece’s health minister.
Greece, which has 11 million people but attracts more than 30 million foreign tourists annually, has identified 13 hospitals across the country for treating infected patients.