Four others were injured inside the store before the suspect fled the scene and attacked a passerby, Zill said.
A sixth man was injured while overpowering the attacker. He was arrested by police shortly afterwards.
And, of course, the Christmas market attack in Berlin last December that killed 12 people.
Germany: Knife attack in Hamburg supermarket kills one
Police say they don't have any information yet on the man's motive.
The motive for the attack was not immediately known, but German media said it could be terrorism-related. "First reports about a possible robbery can not be confirmed so far", he said. Witnesses followed the man and managed to restrain him until police arrived and arrested him.
Police said several people suffered stab wounds and one of the victims was fatally wounded.
A video on its website showed a helicopter landed outside the supermarket with armed police in body armor patrolling the neighborhood.
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