Polish President Andrzej Duda said on social media that he was "shocked by the brutal attack" on a Christmas market in the eastern German city.
"My thoughts and prayers are with the families of the victims and those injured," he added.
The Polish foreign ministry extended its "deepest sympathies to the families of the victims and those who were injured in the attack" in Magdeburg.
"It is appalling that a time of joyful holidays can be turned into a time of tragedy," it added in a post on the X social media platform.
Local officials said there were multiple casualties after a car drove into a crowd of people at a Christmas market in what appeared to be a deliberate act.
Polish foreign ministry spokesman Paweł Wroński said there were no reports of Poles injured in the incident.
German police have arrested a doctor from Saudi Arabia who drove the car, the Reuters news agency reported, citing the premier of the German 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 condolences to the victims and their families.
"My thoughts are with the victims and their families," he wrote in an X post. "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 ploughed into a crowded Christmas market in the German capital Berlin, killing 12 people and injuring dozens of others, Reuters reported.
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Source: Reuters, IAR, PAP