Berlin Police President Klaus Kandt said that officials could not be certain that the man, who was picked up about a mile away from where 12 people were killed and 48 others injured on Monday evening, was the attacker.
Moments before he spoke, German Interior Minister Thomas De Maiziere said that the detainee was "probably from Pakistan" and that he had denied any involvement in the incident.
German authorities are investigating the incident as a terror attack.
- Berlin police say detained man may not have been the truck driver
- Man in custody denies involvement in the attack
- He is identified as an aslyum-seeker likely from Pakistan
- His application for asylum in the country had stalled
- A Polish man found dead in truck was not at wheel when crash occurred
De Maiziere told a press conference that the man in custody had entered Germany on December 31, 2015, and sought asylum in Germany, but that his application had not been completed.
Intelligence and police sources earlier told CNN that the man detained had arrived to the country in Passau, a city on Germany's border with Austria, after traveling through the Balkans.
Berlin police said that the truck, owned by a Polish company, "was steered deliberately into the crowd." It was carrying 25 tons of steel at the time, the vehicle's owner said.
The man in custody was detained by police just more than a mile from the scene. Another man was found dead in the passenger seat of the truck.
Ariel Zurawski, owner of the truck company, told CNN affiliate TVN 24 the vehicle may have been hijacked, as his cousin -- the truck's regular driver -- couldn't have been behind the wheel.
Berlin police corroborated the information, saying the man found dead was a Polish citizen and was not at the wheel during the incident.
De Maiziere said that the man found in the truck appeared to have been shot dead, but that authorities had not found the weapon used.
The minister called for Christmas markets to be closed for a day of mourning. "But to cancel them would be wrong," he said, adding they would hopefully reopen the following day.
Merkel: 'Hard to bear'
German Chancellor Angela Merkel said it would be "especially disgusting" if anyone s in the attack had been given asylum.
Dressed in black and making her first public comments on the attack late Tuesday morning, she called for unity in the country.
"I know that it would be especially hard to bear for us if it was to be confirmed that a person (who) committed this act ... was given protection and asylum in Germany," Merkel said.
"This is a very difficult day. I, like millions of people in Germany, am horrified and deeply sad about what happened yesterday in Berlin."
Monday's attack could cause further political upheaval for Merkel, who has come under criticism over her government's generous acceptance of refugees. Germany has taken in more than 890,000 asylum seekers in the past year, a marked difference to other European nations.
But a backlash has been growing, fueled in part by Islamist terror attacks in Germany and across the continent.
This month, Merkel called for the ban on Muslim full-face veils, in a concession to the right, anti-immigrant wing of her Christian Democratic Union party.
'It felt like slow motion'
At Breitscheidplatz on Monday evening it was a quintessential German Christmas scene: Trees strung with lights, vendors serving candied fruit and waffles, the smell of gluhwein -- German mulled wine -- wafting through the cold December air.
American Shandana Durrani was at the market, at the foot of the Keiser Wilhelm Memorial Church, and had stopped to reply to a text message when the truck rammed into the crowd at around 8 pm.
She was lucky to have stopped, she said, as the truck mounted the curb, mowing people and stalls down just 20 feet in front of her, sending the crowd "running, scurrying, screaming."
"I heard some popping and thought maybe there was a guy with a gun," she told CNN.
"People just started running and dropping their gluhwein."
She said that the it looked as if the driver had just mounted the curb and lost control, and that the whole thing probably lasted a mere 10 seconds.
"It probably didn't last very long, but it felt like it was in slow motion (as I ) tried to get away from it."
The attack bears resemblance to one in Nice, France, in July, when a truck rammed into a crowd gathered to see Bastille Day fireworks, killing 86 and injuring more than 200 people.
Terror groups including ISIS and a branch of Al Qaeda have encouraged their followers to use vehicles to stage attacks.
But no one has so far claimed responsibility for Monday's attack.
Before Monday's attack, both the US and UK governments had warned their citizens of potential security threats in Germany.
The US had issued a blanket travel warning for Europe, saying there was "credible information (which) indicates terrorist groups continue plotting possible attacks."
German officials had also expressed concerns over security for Christmas markets, which are often frequented by large crowds.
Although few details have emerged of the detainee, US President-elect Donald Trump quickly linked the incident to "ISIS and other Islamist terrorists" and "global jihad."
Dominic Thomas, a professor at UCLA who has written on European Union issues, told CNN that another attack by a refugee or immigrant would be "an absolute nightmare" for Merkel.
"It feeds into the discourse of (far-right party) Alternative fur Deutschland, which has been trying to shape the conversation precisely around these types of events."
David Andelman, author of "A Shattered Peace: Versailles 1919 and the Price We Pay Today", said that many Europeans are coming to fear that traditional democratic values are only giving aid and comfort to terrorists, leading to a swell in support for more authoritarian politics.
"Across Europe, right-wing candidates are positioning themselves against immigration and Islam, defending an ever-tougher stance with every new terrorist assault," he said.