Two people were killed by gunshots in a grocery store in Treysa in North Hesse, in the Schwalm-Eder district.
The police announced on Tuesday.
The officials are on site with a strong contingent.
There is no danger to the population, it said.
As the police announced via Twitter, the incident happened shortly after 1 p.m.
"Two people were found dead in the market," officials wrote.
As the "Hessische/Niedersächsische Allgemeine" (HNA) reports, citing a witness, a man is said to have initially followed a woman in an Aldi branch.
She then called out for help, but was then shot by her pursuer.
The man then turned the gun on himself, the newspaper writes.
As the witness described, many customers did not notice the crime at first.
It would have sounded like a glass shattered, the woman told the HNA.
Only then did they realize what had happened.
For several decades, Treysa has been the largest district of Schwalmstadt, which is about 40 minutes by car east of Marburg.
About 18,000 people live in the city.