Roads in Nea Peramos, 27 km (17 miles) west of Athens, turned into fast-flowing rivers of mud, TV footage showed.
"Practically the entire town of Nea Peramos has flooded," Mayor Grigoris Stamoulis told Antenna TV. "I don't think we've ever seen such flooding before."
Stamoulis said efforts were under way to rescue people from their cars and homes but that he did not believe anyone was in immediate danger.
In the nearby town of Mandra, one woman was found dead in her home, the fire brigade said. Twelve people were rescued from a bus on a bridge.
Some residents were forced onto the rooftops and balconies of their homes, state television said. Authorities received at least 160 calls for help.
On Tuesday, Greece declared a state of emergency on the island of Symi after a storm swept cars into the sea, damaged homes and cut off electricity and water supplies.