Police spokesperson Bjoern Reusch told The Associated Press that witnesses said the 21-year-old asylum-seeker, who was known to police, was having an argument with the woman before attacking her about 16:30. The suspect, whose name was not released, wounded another woman and a man as he fled.
Investigators were still trying to determine the motive behind the attack, but Reusch said "there are no indications this was a terrorist act".
The Bild newspaper reported the woman worked at the kebab stand near where confrontation took place.
Some Germans are also fearful of any signs of a rise in crime or lawlessness after the country registered about 1 million asylum-seekers last year.