Reports said police opened fire on a knifeman after he attacked another man in the small west German town of Hagen, close to Dusseldorf and Cologne.
A local reporter said the assailant was holding a "sword" or machete.
A second man is understood to be critically injured in the attack.
The incident followed reports of a shooting at a busy hair salon in Duren.
German media reported that two of the men caught up in the Hagen attack were involved in an altercation, although this has not been confirmed by the police and the exact circumstances are not yet known.
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Initial reports said one of the men worked at an insurance company in the town and the other man was a customer.
An account of the incident said that one of the men had attacked the other with a "sword-like object".
Police arrived and when he refused to drop the weapon, they opened fire.
He later died in the police station, a report on RP Online said.
The second man is said to have been taken to hospital where he is being treated for his injuries.
A photo posted on Twitter by journalist Alex Talash showed several ambulances and a fire engine at the scene.
Germany has been on edge after a spate of attacks this summer, many caused by migrants, sparking an upswell of anger at Chancellor Angela Merkel's open-door immigration policy.
Located in North Rhine-Westphalia, Hagen is about 10 miles south of Dortmund and has a population of almost 200,000.