A further 48 were injured - some seriously - when the vehicle rammed into the market outside the Kaiser Wilhelm Memorial Church on Monday evening.
Security sources believe the driver of the articulated lorry - which had Polish number plates - was an asylum seeker from Pakistan or Afghanistan, thought to have come to Germany in February, German media reported.
A "suspicious person", thought to be the driver, was arrested near the scene, authorities said.
Special forces police are reported to have stormed a refugee accommodation centre in a hangar at Berlin's old Tempelhof airport.
MORE: Wolverhampton witness describes horror of Berlin lorry 'terrorist attack'
Berlin Police said on Twitter on Tuesday morning that the incident was intentional and a suspected act of terrorism.
"Our investigators are working on the assumption that the truck was intentionally driven into the crowd at the Christmas market on Breitscheidplatz," the post said.
"All police measures concerning the suspected terror attack at Breitscheidplatz are being taken with great speed and the necessary care."
The force added: "A suspicious person was arrested near #Breitscheidplatz. Whether it is the driver of the truck, is currently under consideration.
"Currently, there are no indications of further dangerous situations in the city near #Breitscheidplatz."
Witness Mike Fox, from Birmingham, said that the large truck missed him by only about three metres as it drove into the market, tearing through tables and wooden stands.
"It was definitely deliberate," said the tourist.
He said he helped people who appeared to have broken limbs, and that others were trapped under Christmas stands.
The Berlin attack came a week after concrete bollards were installed around Birmingham's Frankfurt Christmas Market as a security measure.
Berlin Police spokesman Thomas Neundorf said a passenger in the lorry - who officials later confirmed was a Polish national - was among those killed.
The truck carried Polish number plates and investigators would work to determine whether it was stolen or driven legally, Mr Neundorf added.
The Polish owner of the truck, Ariel Zurawski, told TVN24 he feared the vehicle may have been hijacked and said "they must have done something to my driver".
Photographs from the scene showed the black lorry askew across a road, surrounded by debris from smashed Christmas market huts and stalls.
Broken remnants of a hut were lodged in the cab's shattered window alongside a Christmas tree, its lights dangling down in front of the lorry's grill.
Eyewitnesses described the "terrifying" moment the lorry careered past tourists and locals who had been shopping and drinking at the market.
Briton Emma Rushton saw the lorry hurtle past her, an incident she said could in no way have been an accident.
Ms Rushton told Sky News: "The stall that we bought our mulled wine from was completely crushed. People were tearing off wooden panels to get out."
She added: "It was not an accident. It was going 40mph, it was in the middle of the market. There was no way that it could have come off the road and it showed no signs of slowing down."
Jan Hollitzer, 36, deputy editor-in-chief of local news outlet Berliner Morgenpost, said the market fell "silent" following the truck attack as shocked visitors looked at the devastation.
He told the Press Association that he had seen "more than one" person lying under the vehicle.
As the incident unfolded, Berlin Police urged people to stay at home and refrain from spreading rumours.
White House National Security Council spokesman Ned Price earlier said the US condemned the incident as an apparent terror attack.
He said: "The United States condemns in the strongest terms what appears to have been a terrorist attack on a Christmas market in Berlin, Germany, which has killed and wounded dozens."
President-elect Donald Trump also branded it an act of terrorism, tweeting: "Today there were terror attacks in Turkey, Switzerland and Germany - and it is only getting worse."
West Midlands councillors also took to Twitter to express their shock.
Wednesfield North's Councillor Phil Bateman MBE said: "I am appalled by the loss of life in Berlin, following perhaps a terrorist attack. Deepest sympathy and condolences to this tragedy."
Councillor John Clancy, leader of Birmingham City Council, said: "Distressing news coming from Berlin this evening. My thoughts go to the city, the victims and their families. Birmingham stands with you."
Foreign Secretary Boris Johnson tweeted his condolences following the "terrible tragedy", while the Foreign Office warned Britons travelling to Germany of a high risk from terrorism.
In advice updated after the crash, it said: "There may be increased security in place over the Christmas and New Year period, including at Christmas markets and other major events that might attract large crowds.
"You should remain vigilant and follow the advice of local authorities."
It is understood the market is a regular festive treat for shoppers and includes stands that offer seasonal foods such as bratwurst, sweet waffles, candied fruits as well as mulled wine and homemade eggnog.
Facebook has activated a safety check feature for travellers and locals on the social network.
A police cordon remained at the site on Tuesday morning, though parts of the Christmas market had been re-opened.
Commuters walked quietly past the wooden stalls and Christmas trees in the market, many of which were still lit up with white lights. White screens were erected around a large part of the area where the articulated lorry came to a stop.
As emergency services prepared to remove the lorry, tributes began to appear nearby. People laid red candles and flowers, while others wept as they passed the scene.
A glass jar with a white candle inside had a note pinned to it, which read: "I am Berlin for more humanity and sympathy."