The police added that there was no danger to the public, according to US news webiste.
The shooting occurred around 1 pm local time (1100 GMT) in Schwalmstadt-Treysa, a town of around 8,500 people northeast of Germany's financial capital Frankfurt, according to police.
They said it was not yet clear what had happened. Regional newspaper HNA cited an eyewitness as saying that a man had shot a woman and then himself at the Aldi outlet.
MP/PR