An asylum seeker has killed a woman with a machete in the south-west German city of Reutlingen, in an incident local police say does not bear the hallmarks of a terrorist attack and was more likely domestic violence.

Three people were also injured in the assault, which ended when the 21-year-old Syrian assailant was hit by a car.

"At this stage of the inquiry we have nothing to indicate this was a terrorist attack," police said following the attack near the bus station of the city near Stuttgart.

They said the attack happened after the perpetrator "had a dispute" with a 45-year-old Polish woman.

After the attack, the suspect briefly went on the run before being struck by a car, allowing officers to overpower him.

The attacker was already known to police for previous acts of violence, a police source said.

German news agency DPA quoted a police spokesman as saying that officers were working under the assumption that the machete attack was "a crime of passion".

German media reported that the attacker and the murdered woman worked in the same Turkish fast food restaurant, where the argument also started.

"According to the information available, the perpetrator acted alone; the people of Reutlingen and its surroundings are very probably not in danger," a police statement added.

News channel NTV said there were scenes of panic in the city centre following the attack, which came just two days after a German-Iranian teenager killed nine people and injured 19 others in Munich, Germany's third-largest city, before committing suicide.

The 18-year-old Munich attacker is believed to have been "obsessed" with mass killers such as Norwegian fanatic Anders Behring Breivik and had no links to the Islamic State jihadist group.

The carnage in Munich also came just four days after a teenage asylum seeker went on a rampage with an axe and a knife on a regional train near the southern city of Wuerzburg, injuring five people.

German authorities said the Wuerzburg attacker was believed to be a "lone wolf" who was "inspired" by Islamic State without being a member of the network.

AFP