He said the suspect was armed with a kitchen knife when he entered the supermarket and started stabbing customers. He was arrested by police shortly afterwards.
A machete-wielding man has gone on a stabbing rampage in a major German city, according to reports.
Earlier, Hamburg's police had tweeted that the attacker appeared to be a robber fleeing the store, before later saying they were unsure of the motive. They are not ascribing a motive to the attack now, with German media suggesting terror and robbery as possibilities.
The motive for the attack was not immediately known, but German media said it could be terrorism-related. They said initial reports about a possible robbery had not been substantiated.
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One attacker has been arrested, but police are looking for a second man, Bild reported.
Several people suffered stab injuries and one of the victims was fatally wounded, officers added.
Newspaper Bild showed a picture of the alleged Hamburg attacker sitting in the back of a police auto, his face concealed with a bloodied shroud.