In a statement, police said they will ensure that there are no movements to and from boarding schools by both pupils and parents.
They will ensure that all visitors to the country comply with the health and safety regulations announced by President Emmerson Mnangagwa on Tuesday.
Mnangagwa said all those coming into the country should have valid covid-19 certificates.
Zimbabwe has been winning the war on coronavirus and has less than 700 active cases mostly in Harare and Bulawayo.
It has managed to contain deaths to 60 only last month, down from more than 800 in January.
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