A firefighter died in the town of Schwaebisch Gmuend while trying to rescue a flood victim, who also died.
In Weissbach a man died when an underground garage was flooded. A girl who took shelter from the rain under a bridge was killed by a train.
The state of Baden-Wuerttemberg was worst hit. Shipping has been halted on the Neckar river.
An Audi car factory in Neckarsulm has suspended work, because parts of the plant are now under water.
Hundreds of cellars have been flooded and mudslides have blocked several roads.
In the town of Braunsbach - one of the worst-hit places - floodwaters swept away two bridges. Dozens of homes there are at risk of collapse and must be evacuated, the daily Frankfurter Allgemeine Zeitung reports.
One official said more rain fell in just a few hours on Sunday than normally falls over months.
About 7,000 firefighters and other emergency workers were called out to deal with the many incidents.
On Saturday lightning strikes injured more than a dozen people in Germany and France and killed a man on a mountain in southern Poland.
Several children were seriously injured by lightning during a birthday party in a Paris park - Parc Monceau.
Four people have died in floods in southwestern Germany after torrential rain in the past 24 hours.