Hamburg knife attacker identified as 26-year-old UAE born male
Police said they were unable to immediately determine the motive behind the attack and were "continuing to investigate every possibility".
Citing security sources, Berlin newspaper Der Tagesspiegel reported that the 26-year-old perpetrator was known to police.
Around 1310 GMT, the attacker stabbed to death a 50-year-old man believed to be a German citizen
Police said that he "struck out wildly" at others, wounding five more in the supermarket, a 50-year-old woman and four men aged 19, 56, 57 and 64.
Another 35-year-old man was hurt while overpowering the attacker in the street alongside other passers-by shortly after the killing.
All of the wounded were being treated or operated on in hospital, some of them for serious injuries, police said.
While the attacker's motives remain unknown, Germany has been on high alert about the threat of attacks, especially since last December's truck rampage through a Berlin Christmas market that killed 12 people.
The Islamic State group claimed responsibility for the carnage in which a Tunisian rejected asylum seeker and ex-convict, Anis Amri, 24, ploughed the stolen truck through a crowd.
It was Germany's deadliest attack by an Islamist militant, but not the first.
In 2016, the IS group also claimed a suicide bomb attack in the southern city of Ansbach which wounded 15 victims, and an Afghan man's axe rampage on a train in Bavaria that hurt five, before the perpetrator was shot dead by police.