Officials said the victims appeared to have been chosen randomly by the suspect, who spoke "incoherently" after his arrest.
"At the moment there are no indications of any immediate relationships between the culprit and the victims," said Bavaria's interior minister, Joachim Herrmann, calling it an "ugly, incomprehensible crime."
Police were alerted at 10 am that a middle-aged man driving a silver Mercedes had opened fire on a woman in the town of Tiefenthal, 50 kilometers west of Nuremberg. The 82-year-old woman died at the scene.
The suspect then fired at a farmer driving a tractor, who was slightly injured by flying glass, and drove to a gas station in Bad Windsheim, 35 kilometers from the scene of the shootings.
"Shortly before noon, police were informed that staff at an Esso gas station in Bad Windsheim had overpowered the man after he threatened them with a weapon," said Herrmann. "It's thanks to the brave intervention of the gas station staff that the suspect was stopped."
G had permits to own two firearms but not to carry or use them, authorities said.
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