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The deceased is a 30 year-old son of a local businessman who had recently returned from the United States.
Mnangagwa announced a series of coronavirus fighting measures which come into force with immediate effect.
Among others, the president announced the closure of the country's borders to all human traffic except for returning residents and cargo.
He said returning residents will be subject to strict screening procedures including rigorous enforcement of the 21-day self-quarantine.
The president also imposed a blanket ban on entertainment and recreational activities, including gatherings around night clubs, bars, beer halls, movie houses, swimming pools, gymnasiums and sporting activities.
He discouraged citizens from undertaking unnecessary travel in and around the country.
Mnangagwa also limited visits to hospitals and clinics to one visit per day involving only one relative per patient while the number of public gatherings for such events as religious fellowships, weddings, conferences and funerals has been limited to 50.
Government, he said, will not at this stage close informal markets but encouraged citizens to limit visits to such markets.
Businesses were also urged to come up with measures to reduce human concentration in their workplaces, with non-essential staff encouraged to work from home.
"I am aware that this curtailment of social activities will be hard on all of us. However, such tough measures have become necessary and unavoidable for our collective safety as a nation," Mnangagwa said.
He said government will conduct rigorous contact tracing of all the people who had come into contact with the infected persons and health personnel and law enforcement agencies will be deployed to help with the tracing operations.
"Additionally, citizens are also encouraged to observe social distancing parameters as spelt out by the World Health Organization," he said.
Mnangagwa last week declared the pandemic a national disaster.