Minister Adam Niedzielski also added that over 17,000 people were vaccinated in 186 points on Saturday alone, compared to 3,000 inoculated last weekend.
"The weekend vaccination deliveries system is working," Niedzielski said.
Poland on Saturday reported 7,412 new coronavirus infections and 369 more deaths, bringing its total number of cases to 1,429,612 and fatalities to 33,213.
Prime Minister Mateusz Morawiecki announced last month that his government had secured vaccines for the Polish population from six leading international drug makers.
In the first quarter of this year, a total of 2.94 million people are expected to be vaccinated for COVID-19 throughout the country.
Frontline healthcare workers are first in line to be inoculated, followed by nursing home residents, people over 70, police, soldiers and teachers.
Citizens over 80 can sign up for COVID-19 shots from Friday. On January 22, registration will open to those in the 70+ age group. Vaccinations for this group are due to begin on January 25.
Poland plans to spend PLN 3 billion (EUR 675 million, USD 820 million) on over 60 million doses of coronavirus vaccines under a national inoculation plan adopted by the government.
Almost 6,000 vaccination sites will be available to citizens as the country rolls out its COVID-19 immunization campaign.