The flooding struck the towns of Mandra, Nea Peramos and Megara, a semi-rural area west of Athens where many factories and warehouses are based.
Television images showed tanker trucks, buses and lorries nearly completely submerged in the muddy torrent snaking through entire neighbourhoods.
The dead included a handful of people who perished inside or near their homes, a truck driver, a hunter, and two men who were carried by the raging water miles (kilometres) away to the sea.
"We have confirmation of seven deaths," deputy regional governor Yiannis Vassileiou earlier told state-run TV network ERT as rain continued to fall.
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"The weather forecast is poor, so we are on alert," he said, adding that "torrents of water" had flooded a highway all the way to the sea.
"A river of debris went through Mandra... This is unprecedented," Vassileiou said.
"Everything is lost, the disaster is biblical," Mandra mayor Ioanna Kriekouki told the station.
"We have people who are trapped... we need machinery to get them out of their homes," said Kriekouki, who was also immobilised in her home.
"Access to the area is difficult, debris has nearly reached the height of homes," said fire department spokesman Yiannis Kapakis.
The deputy governor said rubble-clearing equipment had been moved to the area but could not be used until the water levels subside.
Prime Minister Alexis Tsipras said the deaths had been caused by a "disastrous flood" and expressed deep sorrow for the deaths.
The fire service said it had received more than 300 calls for help and dispatched over 120 firemen to the area.