The attack was carried out by a 21-year-old Syrian asylum-seeker at around 4:30 pm local time near a bus station and did not bear the hallmarks of a "terrorist attack", The Locale (German) quoted the police as saying.
"At this stage of the enquiry we have nothing to indicate this was a terrorist attack," police said in a statement.
The statement added that the man, who was arrested, "had a dispute" with the woman and killed her "with a machete" before injuring a second woman and a man.
The attacker was "known to police". According to the information available, the perpetrator acted alone, the people of Reutlingen and its surroundings are very probably not in danger," the 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 several others in Munich before committing suicide.
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