Some 85.45 percent of voters in the northern canton voted in favour of the change, according to final results published on the cantonal administration's website.
Zurich thus became the first of Switzerland's 26 cantons to take an official stand on the measures adopted by the national police force last year following several violent incidents.
The new measures allow police to boost security around first division football and hockey matches, including restricting the movement of fans.
They would allow identity checks and restrict alcohol sales in certain parts of the stadium.
Police can also ban unruly fans from the stadium area for up to three years, compared to a maximum of one year at the moment.
Nine first division football matches are played in the canton of Zurich each year.
The measures were introduced after a match between two Zurich clubs was halted due to violent fans, who threw firecrackers and smoke bombs onto the pitch.