Police told Agence France-Presse the suspect's vehicle was found abandoned near the Tiergarten park. They launched a manhunt involving helicopters and officers from several German states across the capital.
Police and prosecutors appealed for information on a 21-year-old man identified as Abdul B., warning he may be armed and dangerous.
The suspect was believed to have links to "Islamist circles," police spokesperson Florian Nath said earlier.
The attack occurred shortly before 10 p.m. on Saturday.
A vehicle like a mini-van or an SUV "entered the Tiergarten park and hit several people," police said.
Germany in shock
One person died and 16 others were injured, including three with life-threatening injuries, according to Berlin fire department spokesperson Dominik Pretz.
Around 30 more people were treated for shock at the scene.
Police described the suspect as slender, about 1.9 meters (6 feet 3 inches) tall, with black hair, wearing a black hoodie and white trousers.
Investigators said several people were believed to have been wounded with stabbing weapons and that one or more people were seen leaving the vehicle after the incident.
One witness, who had been near the main Pride stage at the Brandenburg Gate, told AFP that celebrations abruptly ended when police instructed people to leave.
"Go home, please," officers told crowds as emergency crews rushed to treat victims.
The attack revived memories of a series of car rammings and attacks on markets that have shaken Germany in recent years and fueled a fierce debate over security.
Chancellor Friedrich Merz vowed that those responsible for the latest incident would face justice.
In a statement, Merz described the incident as a "horrific act" and said he and Interior Minister Alexander Dobrindt were being kept informed of developments.
Berlin Mayor Kai Wegner condemned what he called a brutal attack on "a gathering for a tolerant and peaceful Berlin."
Police had deployed more than 2,000 officers to secure the event.
Following the attack, additional personnel from across Germany joined the search, supported by helicopters equipped with thermal-imaging cameras.
An AFP journalist at the scene saw numerous emergency vehicles lining a nearby road and a large tent erected as police combed the area.