It said so far seven Southern African Development Community countries have reported confirmed cases of coronavirus.
There are more than 200 000 confirmed cases worldwide as of yesterday, with only 769 from 34 countries in Africa.
There have only been 19 deaths in Africa out of a total of 8 778 across the globe.
The Ministry of Health said a 25-year-old woman was admitted at Wilkins Hospital on her return from Rwanda. The ministry is awaiting the results of tests.
Another woman was admitted at Beitbridge Hospital on Wednesday. She was travelling by bus from Northern Cape to Malawi.
Her results are not yet out.
Zimbabwe has so far banned public gatherings of more than 100 people and has ordered all schools, colleges and universities to close on 24 March.
It also postponed independence celebrations scheduled for 18 April as well as the Zimbabwe International Trade Fair which was to kick off on 21 April.
Parliament was adjourned to 5 May.