News agency dpa said the driver had been arrested following the incident in the eastern city of Magdeburg.
Public broadcaster MDR said at least one person had been killed.
It quoted local government spokesperson Matthias Schuppe as saying it was an attack.
Police said on X that “extensive operations” were taking place at the market.
The market was closed and further reports would follow, police added.
Magdeburg, which is west of Berlin, is the state capital of Saxony-Anhalt and has a population of about 240,000.
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