Reutlingen (Germany) (AFP) - A Syrian refugee was arrested after killing a woman with a machete in the German city of Reutlingen, in an incident police said did not bear the hallmarks of a "terrorist attack" and was more likely to have been a crime of passion.

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

"At this stage of the enquiry we have nothing to indicate this was a terrorist attack," local police said in a statement.

Nevertheless, the drama sparked fresh jitters in a country still reeling from other deadly attacks on civilians in recent days.

Police said the machete attack happened after the perpetrator "had a dispute" with a 45-year-old Polish woman. After killing her, the suspect briefly went on the run before being struck by a BMW, allowing officers to overpower him.

The incident took place at around 4:30 pm (1430 GMT) near the main bus station in the centre of Reutlingen, a southwestern city of some 100,000 near Stuttgart.

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.

The incident sparked scenes of panic in the city, NTV news channel reported, with Germans still on edge following Friday's mass shooting in Munich, where a German-Iranian teenager killed nine people and injured 35 others before committing suicide.

It also came six 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.

While Germany has so far not suffered the type of large-scale terror attacks seen in neighbouring Belgium and France, the train assault was claimed by the Islamic State group, its first attack in Germany.

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- Stopped by BMW -

A police spokesman said he could not confirm a story in the bestselling Bild newspaper that the woman murdered in the machete attack was pregnant.

An employee at the Turkish restaurant told the Stuttgarter Zeitung that the Syrian asylum seeker had arrived in Germany by himself about 18 months ago.

NTV showed amateur video footage of the suspect running away from the scene before cutting to him lying on the ground, his face bloodied and his hands cuffed by police.

Earlier, as he tried to make his escape, he smashed a car windshield with his machete, injuring the female driver. He also injured a young man in the face. Another woman lightly hurt her head when she was knocked over by the fleeing assailant, reports said.

A police spokesman told AFP the drama ended when the man was "hit by a BMW as he fled," but he could not say if the driver had deliberately run the man down, as some media were reporting, or if he had been struck by accident.

Pictures from the scene showed forensic police sealing off the area and erecting a tent over the white BMW. A woman's body was also seen lying on the pavement.

"The perpetrator was fortunately arrested and no longer represents any danger," said regional interior minister Thomas Strobl.

While the latest incident does not appear to be linked to terrorism, the fact that the perpetrator is a recent arrival from Syria could pile pressure on German Chancellor Angela Merkel over her open-door asylum policy.

Germany took in more than a million asylum seekers last year, but the public mood towards the newcomers darkened after migrants were blamed for a wave of sexual assaults during New Year's Eve festivities in the city of Cologne.