Dutch police haven't released the 35-year-old man's identity, and the motive for the stabbing remains unknown.
“We are keeping all scenarios open,” a statement from police said.
The stabbing occurred around 7:45 p.m. in an area teeming with shoppers and close to the city’s most popular nightlife centers.
The three victims -- two 15-year-old girls and a 13-year-old boy -- have spoken to detectives and were released from the hospital late Friday. Police said in a statement that the teens didn’t know one another.
The attack in the Netherlands came hours after a man wearing a fake explosive vest stabbed several people in London, killing two before he was fatally shot by officers. Police are treating the London Bridge attack as a terrorist act.
The Netherlands was shocked by a similar stabbing in Amsterdam a year ago, when two Americans were wounded in a knife attack that prosecutors say had a “terrorist motive.”
Meanwhile, in London on Friday, witnesses said they saw a man with a knife being wrestled to the ground by members of the public on the bridge before officers shot him dead.
Video images showed people spraying the fleeing suspect with a fire extinguisher, while another passer-by held what appeared to be a long white stick. Witness Amy Coop, who was at the Fishmongers’ Hall, said it was a narwhal tusk the man had grabbed from a wall before going to confront the attacker.
The suspect, 28-year-old Usman Khan, was imprisoned six years for terrorism offenses before his release last year.
Khan was attending a program that works to educate prisoners when he launched the attack, killing a man and a woman and injuring three others just yards from the site of a deadly 2017 van and knife rampage.
The Associated Press contributed to this report.