The truck crashed into people gathered around wooden huts serving mulled wine and sausages at the foot of the Kaiser Wilhelm memorial church, which was left as a ruin after World War 2, in the heart of former West Berlin on Monday evening.
"Our investigators assume that the truck was deliberately steered into the crowd at the Christmas market at Breitscheidplatz," police said on Twitter.
"All police measures related to the suspected terrorist attack at Breitscheidplatz are progressing at full steam and with the necessary diligence," police said.
Police said on Twitter that they had taken one suspect into custody and that another passenger from the truck had died.
The man found dead in the truck was a Polish citizen but was not in control of the vehicle, police said. The nationality of the suspected driver, who fled the crash scene and was later arrested, was unclear, they said.
German media cited local security sources as saying that there was evidence suggesting the arrested suspect was from Afghanistan or Pakistan and had entered Germany in February as a refugee.
Local broadcaster rbb cited security sources as saying the arrested truck driver came to Germany via Passau, a city on the Austrian border, on December 31, 2015. It cited the sources as saying the man was born on Janury 1, 1993 in Pakistan and was already known to police for minor offences.
If that is confirmed, it could further worsen sentiment towards migrants in Germany, where more than a million people fleeing conflict and poverty in the Middle East, Africa and elsewhere have arrived this year and last.
The record influx has hit Chancellor Angela Merkel's popularity ratings and boosted support for the anti-immigrant Alternative for Germany (AfD). Senior AfD member Marcus Pretzell blamed Merkel for the attack on Twitter.
Austrian Interior Minister Wolfgang Sobotka said on ORF radio he had told the heads of Austria's regional police forces to intensify surveillance measures, although there was no concrete evidence that an incident was about to happen.
Sobotka also called for biometric and fingerprint checks to be introduced along the Balkan route to better control foreign jihadist fighters' movements.
Berlin police are investigating leads that the truck had been stolen from a construction site in Poland. They have taken the truck for a forensic examination.
"We heard a loud bang," Emma Rushton, a tourist, told CNN. "We started to see the top of an articulated truck, a lorry ... just crashing through the stalls, through people."
Rushton said the truck seemed to be traveling about 65kmh. Asked how many were injured, she said that as she walked back to her hotel, she saw at at least 10.
Pictures from the scene showed Christmas decorations protruding from the smashed windscreen of the black truck. Berlin police said on Twitter they were investigating leads that the truck had been stolen from a construction site in Poland.
Interior Minister Thomas de Maiziere said the circumstances of the crash were still unclear, adding: "I don't want to use the word 'attack' yet although a lot points to that."
The incident evoked memories of an attack in Nice, France in July when a Tunisian-born man drove a 19-tonne truck along the beach front, mowing down people who had gathered to watch the fireworks on Bastille Day, killing 86 people. That attack was claimed by Islamic State.
Government officials have said the country, which welcomed nearly 900,000 migrants last year, many from the war-torn Middle East, lies in the "crosshairs of terrorism".
In mid-October, police arrested a Syrian refugee suspected of planning a bomb attack on an airport in Berlin. The 22-year-old man committed suicide in prison shortly after his arrest.
PEOPLE URGED TO STAY AWAY
A government spokesman said Chancellor Angela Merkel was briefed on the situation by de Maiziere and the Berlin mayor. Police said there were no indications of further dangerous situations in the area and urged people to stay away from the scene.
"I'm deeply shaken about the horrible news of what occurred at the memorial church in Berlin," Foreign Minister Frank-Walter Steinmeier said.
The truck veered into the market at what would have been one of the most crowded times, when adults and children would be gathering in the traditional cluster of wooden huts that sell food and Christmas goods in an annual celebration replicated across Germany and much of Central Europe.
Ariel Zurawski, whose Polish freight company owns the truck, said the driver of the truck did not work for him.
"It wasn't my driver," Zurawski told Polish private broadcaster TVN 24. "I vouch for him, he's my cousin."
Merkel saw her popularity slide a year ago when she welcomed tens of thousands of refugees a day at the height of the influx with the optimistic message "we can do this".
But she has recovered in recent months as the numbers have dropped and she announced last month that she would run for a fourth term next autumn.
She is widely expected to win, but analysts have said the one thing that could undermine her in the run-up to the federal election would be a series of attacks, especially if they are linked to migrants allowed in on her watch.
France said it would increase security at its Christmas markets throughout the country.
