They have also beaten up people wearing red T-shirts, the colour of the opposition Movement for Democratic Change party (MDC), a BBC reporter at the scene says.
Protesters are calling for electoral reform ahead of polls in 2018.
President Robert Mugabe, 92, says he intends to stand again.
Leaders from 18 opposition political parties called for Zimbabweans to march through Harare as part of a so-called "mega demonstration".
The High Court ruled on Friday morning that the planned opposition march could go ahead, a day after police warned that unauthorised demonstrations would not be tolerated.
Public protests have proliferated in recent months, focusing on the dire state of the country's economy.
Most of these have come under the banner of the #ThisFlag movement, inspired by charismatic pastor Evan Mawarire, who has urged non-violent protest over perceived corruption and economic mismanagement
The country's economic crisis has worsened recently, leading to a chronic cash shortage and delays paying civil servants.
Home Affairs Minister Ignatius Chombo blamed a demonstration that ended violently on Wednesday on foreign elements.
"We cannot sit idly while our country is being torn apart by unruly foreign-sponsored agents," Zimbabwe's state-run Herald newspaper quotes him as saying.
Police in Zimbabwe have fired tear gas and water cannon at opposition supporters who had gathered for a protest march in the capital, Harare.