Of the injured, 24 people have been released from the hospital, according to authorities.
Berlin police tweeted early Tuesday that the truck was driven into the crowd in what investigators believe was a terrorist attack.
"This is a difficult day. I am, like millions of people during these hours, horrified and shocked by what happened at the Breitscheidplatz in Berlin," German Chancellor Angela Merkel said in a brief statement on Tuesday.
"We must assume that it was a terrorist attack," Merkel added.
A male passenger in the truck died at the scene, authorities said, and is being counted among the 12 fatalities.
“The man who was found dead in the truck did not control the truck that drove to the Christmas market,” Berlin police said early Tuesday. Police earlier tweeted that the man was a Polish citizen.
Flags flew at half staff across Germany on Tuesday as the country mourned the attack's victims. Christmas markets in Berlin closed for the day and the attorney general announced the beginnings of a criminal investigation.
The perpetrator of the attack is likely still on the loose.
A potential suspect was arrested after the incident, but authorities soon hedged at the possibility that the man, an asylum seeker from Pakistan, was responsible for it. The man was later released from custody, according to a German federal prosecutor.
The truck involved in the incident was stolen in Poland from a building site, the Berlin police tweeted.
"The person who was driving and jumped out of the truck was not my driver. I can vouch for my driver," Ariel Zaurawski, the Polish owner of the truck, told Reuters.
Zaurawski said he believes that the truck was hijacked and that something may have happened to the driver. "I can guarantee the one who was in Berlin center was not my driver. They must have done something to him ... his phone does not answer. A moment ago my wife spoke to his wife. She could not get through to him since [about 4 p.m. local time]. Something is wrong. He should have answered, the more so that it was his wife calling."
The investigation is ongoing, police said.
White House National Security Council spokesman Ned Price described the incident as an apparent "terrorist attack."
"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. We send our thoughts and prayers to the families and loved ones of those killed, just as we wish a speedy recovery to all of those wounded. We also extend our heartfelt condolences to the people and government of Germany," the statement reads.
Price added that the U.S. has offered to aid Germany in the investigation.
"We have been in touch with German officials, and we stand ready to provide assistance as they recover from and investigate this horrific incident. Germany is one of our closest partners and strongest allies, and we stand together with Berlin in the fight against all those who target our way of life and threaten our societies," he said.
"Our hearts and prayers are with the loved ones of the victims of today's horrifying terror attack in Berlin. Innocent civilians were murdered in the streets as they prepared to celebrate the Christmas holiday," Trump said.
He concluded, "ISIS and other Islamist terrorists continually slaughter Christians in their communities and places of worship as part of their global jihad. These terrorists and their regional and worldwide networks must be eradicated from the face of the earth, a mission we will carry out with all freedom-loving partners."
ABC News' Joshua Hoyos contributed to this report.