The Swiss city’s official May 1 celebrations unfolded peacefully, but some 20 people, mostly youths clad in hoods, clashed with police later in the day.
Some 100 riot police blocked off part of the city centre and arrested several people as hundreds of onlookers took to balconies overlooking the streets to watch, an AFP correspondent said.
The clashes went on throughout the afternoon. Zurich police told AFP they did not yet have an estimate on damages.
The annual May Day rally drew some 12,000 people, police said.
May Day often turns violent in Zurich. Last year, police arrested more than 500 people.