A 23-year-old woman found slumped over the steering wheel of her car that had stalled on a flooded highway apparently died of a heart attack, Ekathimerini reported.
The torrential rainfall flooded several roads, with Aegaleo, Nikaia, Haidari and Peristeri in Athens' western suburbs among the worst hit, officials said.
Officials said a vacant building apparently collapsed because of the heavy rains, but no injuries were reported.
Firefighters received more than 400 calls to pump out flooded basements or rescue drivers in stranded vehicles.
Witnesses said they watched parked cars being swept away after the Pikrodafni River overflowed its banks. The Ilissos River also broke over its banks.
The flooding disrupted traffic and led to delays in transit systems, Ekathimerini said.
Some customers also lost power temporarily.
Rosie O'Donnell unveils nearly 50-pound weight loss
Putin thinks Obama would save him if he were drowning