Police say people violated the measures but critics say the government is targeting the opposition.
More than 105,000 people have been arrested in Zimbabwe since March for violating regulations aimed at curbing the spread of coronavirus, police say.
Around 1,000 were arrested in the last two days for “unnecessary movement” or for not wearing face masks, they add.
Restrictions have been eased slightly in the country, where more than 1,500 infections have been confirmed.
Critics accuse the government of using the measures to target the opposition and arrest activists, which it denies.
Opposition and civil society groups are mobilising for nationwide protests on 31 July to demand that President Emmerson Mnangagwa step down.
Under current regulations, all Zimbabweans returning from abroad are required to remain in quarantine for three weeks at a government-approved facility. According to police, a total of 276 people had fled quarantine centres, including some who had tested positive.
Almost 30 of them had been arrested, and would be taken to court for exposing their families and communities to the virus, police added. They included two men who had infected seven members of a family, state television reported.
Police say they intend to step up efforts to enforce regulations arguing that many people have become complacent.
Drinking dens had opened and “beer-drinking binges” were being held in backyards, police said. “We’ll be arresting all these violators,” spokesman Paul Nyathi was quoted by state television as saying.
Zimbabwe’s lockdown measures to combat the spread of coronavirus have worsened the country’s economic and political crisis. The government expects the economy to shrink by 4.5% this year while annual inflation surged to 785% in June.
There are calls for more protests against President Mnangagwa, who appears increasingly intolerant of criticism, BBC World Service Africa regional editor Will Ross reports.
If people take to the streets there are bound to be many more arrests, our editor adds.
Meanwhile, in neighbouring South Africa, police had opened cases against more than 230,000 people who were accused of defying lockdown regulations, official statistics released in May show.
South Africa has so far recorded more than 320,000 cases and 4,600 deaths since March – the highest in Africa. Last week, President Cyril Ramaphosa warned that “the storm is upon us”.