Eleven of the patients, including a 66-year-old man who was in a serious condition, were among a group of 53 people who had recently returned from a pilgrimage to religious sites in Israel and Egypt, the official said.
Health ministry representative Sotiris Tsiodras told reporters that a ban on public gatherings would remain in force in three districts in the south-west of the country, and schools in the same area would remain shut until further notice.
Tsiodras said on Thursday that Greece expected a significant rise in new cases in the coming weeks.
The 66-year old patient was being treated in a hospital near the city of Patras. Some of the new cases were detected on the popular Ionian island of Zakynthos, also known as Zante.