Local officials said the incident left multiple casualties and appeared to be a deliberate attack.
German police have arrested a doctor from Saudi Arabia who drove the car, the Reuters news agency reported, citing the premier of the state of Saxony Anhalt, Reiner Haseloff.
One of those who died was a small child, he said, according to Reuters.
German Chancellor Olaf Scholz offered his sympathies to the victims and their families.
"My thoughts are with the victims and their families," he wrote in a post on the X social media platform. "We stand with them and with the people of Magdeburg. I extend my gratitude to the dedicated rescue teams in these anxious hours."
Eight years ago, a truck driven by a Tunisian asylum seeker with Islamist links crashed into a crowded Christmas market in Berlin, killing 12 people and injuring dozens of others, Reuters reported.
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Source: Reuters, IAR, PAP