Zororo Makamba, a journalist and son of businessman James Makamba, had been reportedly treated in isolation at Wilkins Hospital in Harare.
The African country has so far confirmed two coronavirus cases, with the TV host, famous in his country, having been the second person to test positive for COVID-19.
The country's health minister earlier stated that the nation had registered the first death of a coronavirus patient, identified as a 30-year-old man who had recently returned from a foreign country. The minister did not reveal the identity of the victim.
"He had other concurrent serious medical conditions, which made him vulnerable. I wish to urge the nation not to panic because of this death", the minister told reporters.
The World Health Organisation declared the COVID-19 outbreak a pandemic on 11 March. As of Sunday, the number of global COVID-19 cases surpassed 294,000, with more than 12,900 deaths, according to the watchdog.