The man was admitted to Wilkins Hospital on Friday.
He travelled to New York on 29 February and returned to Zimbabwe via Johannesburg on 9 March but started exhibiting mild symptoms of coronavirus on 12 March.
This progressively got worse until 19March when he consulted his doctor.
The ministry today said it had identified and followed up seven people he had contact with and so far four had tested negative.
It is following up 11 others.
The ministry reiterated that only two cases had so far been confirmed.
The first case, confirmed in Victoria Falls, was showing signs of recovery and is being managed under self-isolation.
Movement for Democratic Change leader Nelson Chamisa yesterday said there were two cases in Harare and his party insists that the Harare City Council, which falls under the party, should release its own figures.