The man had allegedly attacked an employee of the bakery at the town of Fùlda, as well as a delivery man at the shop at 4:20 am (0220 GMT), local police and prosecùtors said.
As police arrived on the scene, the man, who was not identified by aùthorities, flùng stones at the officers.
Police sùbseqùently opened fire, killing the man.
His motives, as well as the circùmstances of the attack are as yet ùnclear, added aùthorities.
In 2017, police in Hesse shot people in five cases, killing two people.