A warrant was issued at midnight. Details were not given but media reports say the suspect is a Tunisian man named only as Anis A., born in 1992.
The Tunisian suspect’s residence permit was found in the truck’s cabin.
The man may have been injured in a struggle with the driver, found dead in the cab. The attack claimed 12 lives in all.
Some 150 police officers are said to be involved in searches in the Emmerich area of North Rhine-Westphalia, western Germany, where the suspect’s permit was issued.
German Chancellor Angela Merkel has met her security cabinet to discuss the investigation into the attack.
The Schengen area covers most EU states plus Iceland, Liechtenstein, Norway and Switzerland.
The suspect is also known to use false names, security sources told German media and Reuters.
His name was given using a German convention whereby suspects are identified by their first name and initial.
The Tunisian is reported to have traveled to Italy in 2012 and then on to Germany in 2015 where he applied for asylum and was granted temporary leave to stay in April 2016.
The suspect is said to be known to police and was briefly detained in August with fake Italian identity documents.
Sueddeutsche Zeitung reports that he moved within the circle of an Islamist preacher, Ahmad Abdelazziz A, known as Abu Walaa, who was arrested in November.
Broadcaster N-TV said measures were “now imminent” in North Rhine-Westphalia but there were no further details.
German Interior Minister Thomas De Maiziere refused to confirm or deny media reports about the man but said that officers were still investigating his residential status.
Some 49 people were also injured when the truck was driven into crowds at the Breitscheidplatz Christmas market.
ISIS said one of its militants carried out the attack but offered no evidence.
Polish citizen Lukasz Urban was found dead on the passenger seat with gunshot and stab wounds.
Investigators quoted by German media say there is evidence that, despite being stabbed, Lukasz Urban wrestled him for the steering wheel.
One official quoted by Bild said it appeared from the post-mortem examination that the driver had survived up to the attack and was shot dead when the truck came to a halt. No gun has been recovered.
Ariel Zurawski, the owner of the Polish transport company, said he had been asked to identify Lukasz Urban from photographs.
Police say they are acting on hundreds of tips from the public and are examining DNA traces from the cab of the truck.
German President Joachim Gauck visited some of the injured on December 21.
Officials released the only detained suspect on December 20, saying there was no evidence to link him to the attack.
ISIS claimed the attack through its self-styled news agency, saying it was “in response to calls to target nationals of the coalition countries”.
Prosecutor Peter Frank told reporters that the style of attack and the choice of target suggested Islamic extremism.
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