Mateusz Morawiecki wrote in a post on Facebook that Poland had 65 people infected per 100,000 inhabitants.
“That is still a lot, but it the first signal of stabilization and proof that our strategy and restrictions are starting to have an effect,” he added.
“What does this mean? We do not have to introduce a national quarantine.”
Morawiecki added: “If in the days ahead we can keep the number of infections at a similar level it will mean we’ve won the first battle with the virus, but there’s still a long war ahead of us.”
Poland on Thursday reported 22,683 new coronavirus infections and 275 more deaths, bringing its total number of cases to 641,496 and fatalities to 9,080.
Tougher measures to battle COVID-19 came into effect across Poland at the end of last week following a surge in cases amid a second wave of the pandemic.
Shopping malls have been ordered to limit their operations until at least November 29, though some retail outlets, such as grocery stores, pharmacies and drugstores, remain open.
Hotels are only able to take in guests on business trips. Theatres, cinemas, museums, libraries and galleries have been told to close temporarily.
With 213 COVID-19 deaths per million population, Poland remains less affected by the coronavirus epidemic than some other countries in Europe, new statistics have shown.
To compare, Belgium has 1,125 deaths per million residents since the start of the pandemic, according to data released by the Polish health ministry this week, while Spain has 841 and Britain reports 724.