About 1,000 have been arrested in the past two days for “unnecessary movements” or for not wearing masks, they add.
Restrictions have been eased slightly in the country, where over 1,500 infections have been confirmed.
Opposition and civil society groups are mobilizing for national protests on July 31 to ask President Emmerson Mnangagwa to step down.
Under current regulations, all Zimbabwe returning from abroad are required to remain in quarantine for three weeks in a government-approved facility. According to the police, a total of 276 people had fled the quarantine centers, including some positive results.
Nearly 30 of them had been arrested and allegedly taken to court for exposing their families and communities to the virus, police added. They included two men who had infected seven family members, state television reported.
Police say they want to step up efforts to enforce regulations by claiming that many people have become complacent.
The den had opened and “binges to drink beer” were kept in the courtyards, police said. “We will arrest all of these violators,” spokesman Paul Nyathi said on state television.
Zimbabwe’s blocking measures to combat the spread of coronavirus have aggravated the country’s economic and political crisis. The government expects the economy to shrink 4.5% this year while annual inflation has risen to 785% in June.
There are demands for further protests against President Mnangagwa, who appears increasingly intolerant of criticism, reports Will Ross, regional director of BBC World Service Africa.
If people take to the streets there are many other arrests, adds our editor.
Meanwhile, in neighboring South Africa, police had opened cases against more than 230,000 people who had been accused of defying blocking rules, official statistics released in May show.
South Africa has so far recorded over 32,000 cases and 4,600 deaths since March, the highest in Africa. Last week, President Cyril Ramaphosa warned that “the storm is upon us.”