One of the dead was a young child, said Reiner Haseloff, premier of the state of Saxony-Anhalt. The incident took place on Friday evening in Magdeburg, the state capital, 150km west of Berlin.
"It is a catastrophe for the city of Magdeburg, for the state and for Germany in general," Haseloff said, adding that the death toll could rise.
Haseloff described the attacker as a 50-year-old male doctor from Saudi Arabia with permanent residency in Germany, where he had lived for almost two decades.
"As things stand at the moment, we are talking about a lone offender, which means that there is no further danger to the city because we were able to arrest him," he said.
Police arrested the suspected attacker, who was described as a doctor from Saudi Arabia. (AP PHOTO)
The motive was unclear. The suspect was not known to German authorities as an Islamist, according to local broadcaster MDR.
Saudi Arabia's foreign ministry condemned the attack.
Following the incident, police cleared an area surrounding the vehicle to investigate a possible explosive device, local broadcaster MDR reported. It later cited police as saying that no such device had been found.
A police operation was also under way in the town of Bernburg, south of Magdeburg, where the suspect is believed to have lived, local newspaper Mitteldeutsche Zeitung reported.
Police were not immediately available to comment on the reports of a suspicious item or the operation in Bernburg.
German Chancellor Olaf Scholz, who sent his thoughts to those affected in a post on X, is expected to visit the scene on Saturday together with Interior Minister Nancy Faeser.
As news of the attack broke, Elon Musk, the billionaire allied with US President-elect Donald Trump, criticised Scholz and called on him to resign.
A video posted on social media from a position above the market shows a car driving at speed through a crowd walking between two rows of market stalls. People can be seen knocked to the ground and running away. Reuters was able to verify the location, with the trees, outline and design of the buildings matching file and satellite imagery of the area.
A view of the cordoned-off Christmas market in Magdeburg, Germany. (AP PHOTO)
Footage from a local broadcaster showed people wrapped in blankets on the ground receiving care in the wake of the attack.
Bild newspaper quoted a witness named only as Nadine saying she had been walking arm-in-arm with her boyfriend, Marco, when the car came hurtling towards them.
"He was hit and ripped away from my side," Bild cited her as saying, adding he had been injured on his leg and head and taken to hospital but she did not know where to find him.
"The uncertainty is unbearable," she told Bild.
Eight years ago, Anis Amri, a failed Tunisian asylum seeker with Islamist links, rammed a truck into a crowded Christmas market in Berlin, killing 12 people and injuring dozens of others.
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