Health Minister Obadiah Moyo said returnees from South Africa and Botswana were now the biggest threat since some were avoiding official border posts and sneaking back into the country without being tested or quarantined.
Some of those at the isolation centres are also escaping.
Zimbabwe has tested 38 352 people so far. Twenty-five have recovered from the virus.
The country is under a national lockdown which was extended indefinitely but will be reviewed every two weeks with the first review expected this Sunday.
Globally there are now 5.7 million cases with 2.9 million active ones.
There have so far been 352 700 deaths with the United States leading at just over 100 600 deaths.