Two people have been killed in a shooting at a supermarket in the central German city of Schwalmstadt.

Two people were found dead after a shooting in a supermarket north of Frankfurt, authorities said Tuesday.

According to local police, gunfire was reported at the premises in Schwalmstadt at around 1 p.m. local time (1100 UTC).

A police statement said a 58-year-old man is believed to have shot a 53-year-old woman inside the discount grocery store before turning the gun on himself.

Police said an investigation into the motive behind the shooting was underway.

"There is no danger to the population," a police statement said, adding that there was a heavy police presence at the scene.

Schwalmstadt is a rural mid-sized town of just under 20,000 people roughly 90 minutes' drive north of Frankfurt.