In a statement, they added they had yet to determine the nationality of the perpetrator, who stabbed to death a 50- year-old man believed to be a German citizen, and wounded six.
All of the wounded were being treated or operated on in hospital, some of them for serious injuries, police said.
Five people suffered knife wounds, comprising a 50-year- old woman and four men aged 19, 56, 57 and 64.
A 35-year-old man was hurt while overpowering the attacker in the street alongside other passers-by shortly after the killing.
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The Berlin newspaper Der Tagesspiegel said the knifeman was a known Islamist, but police did not immediately respond to the report.
In addition, there were eyewitness reports that the man shouted "Allahu Akbar" (God is greatest) as he fled the scene.
"We continue to investigate every possibility," the police statement said.