The attack took place shortly before 8.30am on Thursday.
The suspect, who was arrested five minutes after emergency services were alerted, is a 31-year-old Swiss-Turkish dual citizen who lives in Winterthur, regional police chief Marius Weyermann said.
He had come to authorities' attention in 2015 for distributing propaganda of the Islamic State group, Weyermann added.
In recent days, he was taken to a psychiatric facility after calling the police emergency number and making "confused comments," but he left on Wednesday after a doctor determined that he was not dangerous.
Three Swiss men, ages 28, 43 and 52, were wounded in Thursday's attack.
The first two were discharged or were about to be released from hospitals by mid-afternoon, Weyermann said.
The oldest was still hospitalised after an operation on a thigh injury.
Weyermann said investigators believe the man acted alone.
Mario Fehr, the Zurich region's top security official, described the attack as "an evil act of terror".
He said the suspect was born in Switzerland and gained Swiss citizenship in 2009, and apparently had spent much of the last two years in Turkey.
Winterthur has about 123,000 residents and is located in northeastern Switzerland, near the country's biggest city Zurich.
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