The three children hurt in the attack were treated by paramedics and taken to hospital.
The attack happened around midday on Berninastrasse, a largely residential street in the Oerlikon district in the north of Switzerland's biggest city.
"According to initial findings, a daycare worker was on her way to a daycare centre with several children when a man suddenly attacked the children with a blade," Zurich police said in a statement.
"The daycare worker reacted immediately and overpowered the attacker with the help of a man, and held the suspected perpetrator until the emergency services arrived."
Police said a 23-year-old Chinese man was arrested and taken to a police station.
"One seriously wounded boy and two moderately injured boys aged five were given first aid" by emergency services "and then taken to hospital", the statement said.
Forensic specialists were called in and further investigations are being carried out by police, while police psychologists and a care team were deployed to look after those affected.
No other people were injured, police spokesman Pascal Siegenthaler told AFP.
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