The pair arrived at the 51-year-old man's house in Lower Saxony to accompany a doctor and a local official when they went to see the man, who had become violent after stopping his medication.
When the police entered the isolated farmhouse the man shared with his mother, he charged at them with a hammer, allegedly hitting one officer on the head several times.
The other officer shot the victim three times, killing him. His mother was not home.
A post mortem will be conducted, while the Oldenburg state prosecutor is investigating whether the police officer who shot the man was acting in self-defence, a spokeswoman said that evening.
A reconstruction of the incident would, she said, help the prosecution decide.