Riot police were on patrol in the capital to prevent crowds gathering after civil action groups vowed to hold the first anti-government protest in several weeks.
Frustration at Zimbabwe's economic collapse under the authoritarian regime of Mugabe, 92, has triggered a series of protests this year, with security forces often beating up demonstrators.
Sylvanos Mudzvova, one of the protest leaders, told AFP that fellow activist Patson Dzamara and two others were admitted to hospital after being abducted by unidentified men who dragged them out of their cars.
"Three others are unaccounted for. They were blocked on the road and taken from their cars which were later found burnt.
"This is the most barbaric thing to do. That's not the way to stop dissent."
Zimbabwe police were unavailable to comment.
Mugabe, who has held power since 1980 and is increasingly frail, has often used brutal force to silence his opponents, and has previously warned the protesters they were "playing a dangerous game".
The planned demonstration was to focus on government attempts to print its own "bond notes" currency -- equivalent to the US dollar -- to tackle the country's severe cash shortage.
The nation's economy has been hollowed out by endemic corruption, drought, and government policy including land seizures and laws forcing foreign-owned companies to sell majority stakes to locals.
Banks are scarcely able to dispense cash, and the government has repeatedly failed to pay soldiers and civil servants on time.
Unemployment is at about 90 per cent, and thousands of companies have closed in the last three years.
The government says the new currency will be gradually introduced from later this month, but the date has been delayed several times.
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