But mining and manufacturing operations will be exempted – to keep the economy running.
The lockdown was due to expire midnight on Sunday.
In a live broadcast, the president said the conditions for lifting the restrictions had not been met.
He described the extension as a hard decision made reluctantly, but one that was necessary and unavoidable.
Zimbabwe has recorded 25 coronavirus cases and three deaths, amid warning by the World Health Organization (WHO) that Africa must prepare for an increase in infections.
The country is still battling to increase mass testing and the number of treatment centres.
The WHO has warned of difficult times ahead but cautioned countries against lifting restrictions prematurely.