The industrial towns of Mandra, Nea Peramos and Megara, west of the capital Athens, were the most affected.
Many of the dead were elderly people whose bodies were found inside their homes, reports say. Fast-flowing torrents of red mud flooded roads.
"Everything is lost. The disaster is biblical," Mandra Mayor Yianna Krikouki told state broadcaster ERT.
At least 13 people have been taken to hospital, and some are still missing.
Prime Minister Alexis Tsipras has expressed his condolences.
Heavy rain has hit parts of Greece for about a week.