The ramming attack happened in the Tiergarten park near the Brandenburg Gate about 10pm on Saturday, not far from one of Europe's biggest annual LGBTQ celebrations, Christopher Street Day.
One person was killed and 29 were injured, authorities said.
"About 6pm, the suspect involved in yesterday's attack in Tiergarten was located at an allotment garden complex in Spandau," Berlin police wrote on X.
"According to initial findings, he ran towards officers while armed with a bladed weapon; police ... subsequently opened fire. Despite immediate resuscitation efforts by the Berlin Fire Department, he died at the scene."
A federal prosecutors spokesperson confirmed one person had been shot and declared dead.
Berlin police had identified the suspect as Abdul B, 21, and published his picture, asking the public for information on his whereabouts.
The suspect had "attracted attention in the past through a high number of criminal offences, through radicalisation, through membership of the Islamist scene," Interior Minister Alexander Dobrindt said earlier, adding that he was a German citizen of Lebanese heritage, born in Germany in 2005.
Berlin mayor Kai Wegner, standing next to Dobrindt, said the incident was "probably an Islamist terrorist attack on our way of living alongside one another, on our liberal democracy, our openness and our freedom".
Afterwards, Wegner praised the police for their "great success" in finding and stopping the suspect.
"The fact that Berlin police have the suspect within 24 hours is a great success for the investigating authorities," the mayor told public broadcaster RBB on Sunday.
"I am very grateful for that," Wegner said.
German Chancellor Friedrich Merz called on people not to be intimidated and divided by the attack.
Such criminals and extremists have no place at the heart of our society, Merz said in Berlin shortly before a memorial service on Sunday.
"We are more, we are stronger," he said.
"These acts have only one purpose: they want to divide our society, they want to take from us the most important thing we have - namely our openness and our freedom," Merz said.
Security sources told Reuters the suspect had been released from juvenile detention only two months ago.
They said he was known to domestic intelligence and was among the hundreds of people classed as potentially dangerous, a label that usually leads to scrutiny or monitoring.
After mowing people down with the vehicle, the attacker injured some with a bladed weapon, thought to have been a machete, Dobrindt said.
The fire service said overnight that three of the injured were in a life-threatening condition.
It was unclear whether the perpetrator had acted alone, since police said more than one person may have got out of the van.
Reuters TV footage from the scene on Sunday morning showed a white mini-van crumpled into a tree.
The mass-circulation newspaper Bild said it was a delivery vehicle that Abdul B had rented.
Hundreds of people gathered at Berlin's Brandenburg Gate on Sunday to mourn the victims of the attack.
The attack comes at a sensitive time for conservative Chancellor Merz's unpopular coalition government, which is going through a bruising cabinet reshuffle as critics accuse it of being ineffective.
State elections take place in two months, with the nationalist populist opposition party Alternative for Germany (AfD) campaigning on issues including immigration and security in a bid to secure control of a regional government for the first time.
with DPA
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