The suspected driver of the car had been arrested, broadcaster MDR and other local media said on Friday, citing a local government official.
A video published by newspaper Bild showed people trying to help what appeared to be multiple injured victims.
"I estimate there are at least 20 ambulances here, a lot of firefighters, and I can see the police helicopter circling in the sky," an MDR reporter said during a live broadcast, adding that there were a lot of armed police on site.
Eyewitnesses told MDR the car drove straight into the crowd, in the direction of the town hall.
"This is a terrible event, especially now in the days before Christmas," head of Saxony-Anhalt state government Reiner Haseloff told MDR, adding that he was on his way to Magdeburg.
Police and the local government's spokesperson were not immediately available for comment.
Eight years ago, a truck driven by Anis Amri, a failed Tunisian asylum seeker with Islamist links, crashed into a crowded Christmas market in Berlin, killing 12 people and injuring dozens of others.
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