The restrictions have so far borne fruit as transmission has not been widespread and numbers remain lower than had been initial projections, he added.
From more than 25,000 tests conducted, the country has so far detected 42 cases, four of which proved fatal.
“This may suggest that despite the small numbers tested, our country might have a reduced COVID-19 trajectory,” he said in a speech broadcast on public television.
Other, similar sub-Saharan countries had recorded similar trajectories, he added.
“Zimbabwe will therefore continue on … lockdown for an indefinite period. We shall have two-week interval reviews to assess progress, or lack of it.”
Zimbabwe imposed its lockdown on March 30.
Local doctors have warned that Zimbabwe’s poorly equipped health service could not cope with a coronavirus pandemic.