A fugitive, who is said to have previously killed his father in Rhineland-Palatinate, hit four cyclists with a car in Mannheim on Sunday evening.
A 71-year-old cyclist was fatally injured, three other people were seriously injured, the police and prosecutors reported on Sunday evening.
The alleged perpetrator is 36 years old.
After his collision with several cyclists, the man is said to have left his car to jump into the Rhine.
The police were then able to arrest the man.
He is probably in a mental state of emergency.
A police helicopter and the water police were also deployed in the search for the alleged perpetrator.