The police have detained the driver, who security sources reportedly say is a 23-year-old Afghan or Pakistani asylum seeker, according to the BBC.
He arrived in Germany in February as a refugee, the DPA news agency said.
The daily Tagesspiegel said the man was known to the police for minor crimes, but not terror links.
“All police measures related to the suspected terrorist attack at Breitscheidplatz are progressing at full steam and with the necessary diligence,” Berlin Police said on Twitter.
Die Welt (Welt.de) reported that one of Christmas market visitors helped the police detain the driver as he was following the attacker to the local park while speaking to the police on his mobile phone.
“It was really the witness who have made it possible to detain the man,” said Winfrid Wenzel, spokesman for the Berlin police.
The edition also reported that German special forces had raided a hangar at Berlin’s Tempelhof airport where they believed the suspect had been living in a shelter before the attack.
It should be recalled that the truck loaded with steel beams plowed into the Christmas market at Breitscheidplatz near the main shopping street in Berlin’s west at 20:14 local time (19:14 GMT), It crashed through wooden huts and stands packed with tourists and locals.
According to the DPA news agency, police believe the lorry drove 50-80 metres (160-260 ft) through the market area.
Police also confirmed that a passenger was found dead in the lorry, and said he was a Polish national. There are fears he may have been the original driver of the vehicle, and that he was subject to a hijacking.
Ariel Zurawski, the Polish owner of the lorry, confirmed that his driver was missing and had been unreachable since 16:00 (15:00 GMT) on Monday.
“We don’t know what happened to him,” he told the AFP news agency. “He’s my cousin, I’ve known him since I was a kid. I can vouch for him.”
The truck was registered in Poland and police said it was believed to have been stolen from a building site there, the Associated Press news agency reports.