The slain woman was shot dead in Tiefenthal, a district in the town of Leutershausen.
The rampage continued when the gunman shot a cyclist before a farmer and another motorist, police said.
After a manhunt, the suspect was detained at a service station.
An armed person opened fire from a silver Mercedes-Benz cabriolet before speeding off, said police spokesman Bert Rauenbusch, according to Bloomberg.
Geman police will hold a press conference this afternoon, says Melanie Hall in Berlin.
He was apprehended a short time later, police spokeswoman Simone Wiesenberg told n-tv television.
The driver first shot and killed the woman, aged 82, before fleeing the scene.
REUTERS/Michael DalderGerman policemen with machine guns walk away from the Carolinum school in Ansbach near Nuremberg September 17, 2009.