“We will be slowly unfreezing the economy from April 19,” Szumowski told private radio broadcaster RMF FM.
He added that a series of government-imposed restrictions on daily life in Poland had proved effective.
"If it weren't for that, we would have tens of thousands of people ill today" with the coronavirus, he said.
A total of 7,049 people have tested positive for the COVID-19 disease in Poland, with 251 deaths from the coronavirus so far, officials said on Tuesday morning.
The number of new virus cases rose by 117 from the previous day, while the death toll increased by six, according to public health authorities.
In a move to contain the spread of the epidemic, the government has limited the operations of shopping malls and closed all pubs, clubs and entertainment venues.
Public gatherings of more than two people have been banned.
Health and government officials have urged Poles to stay home and practice social distancing.
An initial two-week closure of the country’s schools has been extended until April 26.
The government at the end of last month announced tough new restrictions on daily life, banning children under 18 from leaving home unless supervised by an adult, closing parks and beaches, and ordering most hotels to shut.
Poles will from April 16 have to wear face masks or scarves covering their nose and mouth when out in public.