Pictures from the Greek capital show abandoned vehicles standing in deep bodies of water and fleeing residents.
Greek authorities have urged residents in the affected areas to stay away from the streets.
Several livestock animals are also said to have drowned on the island of Corfu, where landslides caused by the storm also blocked the roads, writes Reuters.
Helicopters must have been deployed to evacuate residents on the island.
The island of Evia, which was ravaged by heavy forest fires this summer, has also been hit hard by the rain.
On Saturday, the rain is expected to subside, writes AP.
See photos from the floods in the clip above.