In the run-up to the launch of a nationwide inoculation programme, Niedzielski said that 98.5 percent of the population had a guaranteed opportunity to get vaccinated, while work to set up vaccination points in the remaining districts was underway.
Vaccinations in Poland will be free and voluntary.
The first batch of coronavirus shots are expected to arrive in the country on Saturday, and the first 10,000 Polish citizens are set to be inoculated a day later.
Priority will be given to healthcare staff, followed by pensioners in care homes, people over 60, police, soldiers and teachers.
The first person to receive a shot in Poland will be a female nurse at a hospital run by the interior ministry in Warsaw, while the second will be a male doctor at the same hospital, an official said.
Some 300,000 healthcare workers have already signed up to be vaccinated in the first stage of a nationwide inoculation programme, public broadcaster Polish Radio reported.
Poles who are in non-priority groups will be able to sign up for COVID-19 shots from January 15, according to Niedzielski.
The European Medicines Agency (EMA) on Monday recommended conditional approval for a coronavirus vaccine produced by US pharmaceutical firm Pfizer and its German partner BioNTech for use across the European Union.
The decision by the EU regulator was later in the day greenlighted by the bloc’s executive, the European Commission.
Poland on Wednesday reported 12,361 new coronavirus infections and 472 more deaths, bringing its total number of cases to 1,226,883 and fatalities to 26,255.