"The suspect was overpowered with the help of a citizen ... As his leg was injured, he was taken to a hospital," police said in a post on social media platform X.
They said they had no further information on the condition of the victims.
The motive of the assailant was unclear and remained under investigation, police added.
Police originally said five people were injured in a knife attack.
Emergency services responded quickly, with a rescue helicopter landing on Dam Square which is the central square in front of the royal palace.
Police said that the attack took place on a nearby street about 3.30pm.
The square was cordoned off and reopened after about two hours.
Witnesses said that the alleged perpetrator had apparently stabbed people at random.
They described the suspect as a young man with short blonde hair.
A woman told Dutch radio that the attacker had stabbed a young woman in the back.
The woman was standing by the road with her bicycle.
"The knife was still in her back," the witness said.
The perpetrator then ran away.
A city council meeting involving Amsterdam mayor Femke Halsema was interrupted because of the stabbing.
with DPA and AP
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