"A vehicle entered the Tiergarten park and hit several people and injured them" just before 10:00 pm, police posted on social media, later adding that they were hunting for the occupants of the car.
Police spokesman Florian Nath said some of the survivors had been "seriously" injured and were being treated by the emergency services.
Police told AFP they had found the car they thought had been involved in the incident abandoned in the Tiergarten park.
The Gay Pride event was cut short and police told participants to "Go home, please" and sealed off the area where the people were injured.
An eyewitness by the main Pride stage at Brandenburg Gate said the crowd complied with the request to leave and head away from the park shortly at around 11:00 pm.
The programme at the main stage had been scheduled to continue until midnight.
An AFP journalist in the area saw at least 10 emergency service vehicles at the scene and a tent set up in the road.
Police officers could be seen patrolling the huge area of the park.
Speaking about the attack, the mayor of Berlin, Kai Wegner, said Sunday that the city's "freedom has come under attack in the most horrific way."
Violent attacks
Earlier Saturday, hundreds of thousands of people took part in the event, called Christopher Street Day in Germany.
The march ended next to the Brandenburg Gate, which has been the venue for concerts since Friday.
Germany has in recent years seen several violent attacks at public spaces.
The deadliest such attack in recent years was a truck rampage at a Berlin Christmas market in December 2016 that killed 12 people.
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