Germany's Bild newspaper cited an investigator as saying: "(This was) by no means an accident - someone on the rampage, an ice-cold killer."
But the city's state interior minister, Iris Spranger, denied there was a confession letter, instead claiming placards were apparently discovered in the vehicle.
A 29-year-old man, believed to be the driver, with German-Armenian dual citizenship has been detained, Berlin police told Sky News.
Berlin police spokesman Martin Dams said earlier it is unclear whether the incident was an accident or the driver had intentionally driven into the crowd.
The man had been driving a small Renault car, Bild reported.
According to witnesses, he initially ran away and was stopped and handed over to police, it added.
It identified the victim as a teacher who was in the street with a group of her pupils.
Footage of the scene showed the silver car had crashed into the window display of a department store.
The fire service said about 30 people were injured in the incident - five with life-threatening injuries.
Blankets covered what appeared to be a body in a cordoned-off area guarded by police.
Large numbers of paramedics and ambulances were at the scene.
Reporting from the scene, Sky News' Europe correspondent Siobhan Robbins said the car went down the street and then hit a group of people, went back on to the road, mounted the kerb again before crashing into a shop.
It took place at about 10.30am on Rankestrasse, near the main shopping district's Breitscheidplatz, the scene of the 2016 Christmas market attack in which 11 people were killed.
This is also near the war-ravaged Kaiser Wilhelm Memorial Church, one of the city's best-known landmarks.
Actor John Barrowman, who was at the scene with his husband Scott Gill, told Sky News he saw "a dead person in the middle of the road, covered up".
"The person came on the pavement by the Levi's store and the bank, then drove onto the street, hit the person and killed them in the street, then came back onto the kerb, went down the kerb, through the cafe area and then into the storefront," he said.
"How horrible that this morning these people got up to just go through a regular day, they were going through their daily business. I mean we were shopping, but if you think if we'd have come out of that store one minute earlier..."
"There are hundreds of emergency services that are in the area, blocking city block after city block, off. The cordon keeps expanding."