Officers were alerted to the incident in the Oerlikon district of Switzerland's biggest city shortly after midday. Police said the children were on their way to the day-care center with a woman who works for the facility when the man suddenly stabbed them.
The center employee quickly overwhelmed the assailant with the help of another man and held him until police arrived. Police said the suspect is a 23-year-old Chinese national.
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Three 5-year-old boys were taken to hospitals, one with serious injuries and two others with injuries of medium severity, police said in a statement.
Police gave no details on a possible motive for the attack.