Local media, citing police at the scene, said first indications pointed to a deliberate attack on the market.
Berlin police said 12 people were killed in the crash. Forty-eight people have been taken to hospital with injuries.
Video footage from the scene showed stalls knocked over and people lying injured on the ground. Police cars and ambulances converged on the scene.
The incident occurred at Breitscheidplatz, near the fashionable Kurfuerstendamm avenue in the west of the city.