A machete attack Sunday by a 21-year-old Syrian asylum-seeker which killed one woman and injured two people in a southern German town did not bear the hallmarks of a "terrorist" attack, police said.

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

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, police stated.