Speaking in an interview with state news channel TVP Info, Niedzielski said that making predictions about the pandemic was "fraught with huge risk."
But he said the number of COVID-19 infections in the country was set to rise in the weeks ahead as the summer ends and the Delta variant of the coronavirus begins to spread more quickly.
"It's not a question of if the fourth wave of infections comes, but when it reaches its peak," Niedzielski told TVP Info.
"At the moment, we expect that daily cases may total 1,000 in late September ... and up to 5,000 by the end of October," following people's return to schools and workplaces," he added.
Even so, he told the broadcaster, the government hopes the number of those hospitalised "will not be excessive," thanks to the national vaccination programme.
To date, a total of 36,391,474 vaccine doses have been administered in Poland, with 18,860,734 people fully jabbed.
The health ministry on Friday reported 349 new COVID-19 infections nationwide, up from 258 a week earlier and 164 a month earlier.
Niedzielski said the vaccine infrastructure was extensive and the government "has had done everything" to bring the jabs within easy reach of everyone.
"It's really a matter of choice now," he reflected.
Niedzielski also noted that close to 60 percent of the Polish population was now fully vaccinated, which he described as "a success by Polish standards."
Among those aged over 70, who are at most risk for severe COVID-19 complications, the proportion of those fully inoculated has surpassed 80 percent, representing a natural barrier to the spread of COVID-19, he said.
Meanwhile, "continued efforts are being made" to entice younger people to take the jab, Niedzielski also said in the interview.