Mateusz Morawiecki’s announcement came in the wake of one such incident in the central town of Grodzisk Mazowiecki last week.
As he addressed reporters at a press conference on Monday, Morawiecki revealed that another "thuggish attack" was committed the previous night in the southeastern city of Zamość, where "a man set fire to the local office of the State Sanitary and Epidemiological Service" and to a vaccination centre.
"As we can see, such incidents are sadly occurring repeatedly," he told reporters.
He also mentioned a “case of violence” in the Tri-City area of Gdańsk, Sopot and Gdynia on Poland's Baltic coast.
"All of these acts are going to be very stringently punished in line with the current regulations," Morawiecki said.
“But we will also be taking action to make all the vaccination sites safer, because they are doing a very good job for Poland," he added.
Health Minister Adam Niedzielski was set to visit Zamość later on Monday, along with the country's chief public health inspector and the head of regional police, according to Morawiecki.
National police chief Jarosław Szymczyk announced that, under his orders, a special task force had been set up and was already at work to "identify and arrest the perpetrator of this extraordinarily outrageous, thuggish attack" in Zamość.
Szymczyk also said that vaccination centres around the country “will now receive round-the-clock protection.”
The earlier incident in Grodzisk Mazowiecki happened when a group of people from an organisation called "Polish Yellow Vests" tried to force their way into a vaccination site, whose staff refused to let them in, state news agency PAP reported.
The organisation claims to fight for freedom and oppose "the lawlessness of the government and police." It posts content on social media to discourage the public from taking COVID-19 shots.
Morawiecki told reporters that some of the assailants in Grodzisk Mazowiecki had made punishable threats and had been detained as a result.
"We will be exceptionally strict with such acts," he declared.
He also said that the national vaccination campaign was vital for saving human lives and constituted "a barrier to the fourth wave" of the coronavirus.