Officers in Fulda responded to an early morning call about the incident outside the business in the city about 100km (60 miles) northeast of Frankfurt.
When they arrived, they say the man attacked them with stones and a truncheon. He was shot dead.
Police said the bakery was not open at the time of the incident and that the victims were employees and a delivery driver. Some suffered serious injuries.
Hesse state police and Fulda prosecutors are investigating.
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