The suspected attacker’s motive is unclear, and he has no known links to Islamist extremism.
Footage from the scene shows numerous emergency services vehicles attending while people lay on the ground.
Unverified video on social media purports to show a car ploughing into the crowd at the market.
A spokesperson for the city of Magdeburg said all hospitals in the area were preparing for a “mass casualty event”, according to the Reuters news agency.
City officials said around 100 firefighters and 50 rescue service personnel are at the scene.
German Chancellor Olaf Scholz said reports from Magdeburg “lead us to fear the worst”.
He added: “My thoughts are with the victims and their loved ones. We stand by their side and by the side of all Magdeburg residents. My thanks to all the emergency services in these difficult hours.”
Scholz will visit the city on Saturday, Haseloff said.
Around 19:20 local time (18:20 GMT), the organisers of the Christmas market announced that it had been closed as asked “for understanding”.
A short while later, they called for members of the public to avoid the market. “Please let the emergency services do their job and leave the market in an orderly manner,” they wrote on social media.
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