A rare type of tropical storm known as a Medicane began on Saturday and has so far mostly affected areas on the island of Evia, east of mainland Greece, and the southern Peloponnese peninsula.
State TV said that a young man and a middle-aged couple were missing in Evia.
The civil protection service said that it had launched a search and rescue operation near the town of Mantoudi.
Ships were held at Greece’s main ports and traffic was disrupted in many other areas across the country as roads flooded because of the heavy rain.
Gale-force winds led to power cuts and falling trees across the country.
Firefighters have so far received more than 1,300 calls for assistance to help evacuate people trapped in cars and flooded homes and to remove downed trees and other debris.
TV images showed flooded streets turned into rivers in the wider area of Corinth in the Peloponnese and massive sea waves crashing into the shores of coastal towns in the region.
“The Peloponnese is holding on despite the impact and the side effects of this extreme weather phenomenon,” said regional governor Petros Tatoulis, adding that homes, fields and state infrastructure had suffered damage.
Temperatures plunged unexpectedly by up to 10 degrees Celsius this week.
Wind speeds topped 100kph in several areas and were forecast to intensify.
The civil protection service warned that northern and central Greece could also be affected on Sunday and called on citizens to take self-protection measures.
Authorities were also concerned that the tropical storm could bring mudslides and floods in the wider Athens area, which was recently hit by deadly fires and flash floods.
In August blazes in the area of Mati killed at least 99 people.
Last year 24 people were killed and scores were left homeless after a rain-swollen torrent swept through two coastal towns west of the capital.
