A bystander overpowered the suspect who was injured in the leg, police said in a statement on X.
The suspect “is receiving medical care and will be questioned at a later stage”, said the police spokesman.
Police erected a cordon around the area where the stabbings took place, near the central Dam Square, where a trauma helicopter had landed to take victims to hospital.
An AFP reporter on the scene said the injured had been evacuated from the location but there was still a heavy police presence and ambulances were also on hand.
The police spokesman was unable to give information about the condition of the wounded.
Early images from local news agency ANP showed a person on a stretcher being loaded into the back of an ambulance.
Public broadcaster NOS showed images of police pushing someone on a stretcher while hooked up to an intravenous drip.
According to local media reports, Amsterdam mayor Femke Halsema left a meeting in the town hall when news of the attack broke.
The police urged anyone with images of the incident to upload them as evidence. They also called on people to avoid the area and let them carry out their investigation.
Local media Het Parool cited a witness Marco Schoenmaeckers as saying that he saw one of the victims.
“I saw a knife of at least 10 centimetres sticking out of the girl’s back, between her shoulders,” Het Parool quoted Schoenmaeckers as saying.
- Agence France-Presse