Szymczyk told public broadcaster Polish Radio that "it is just a matter of time" before the man is detained as police have published a video from CCTV cameras from the site of the arson attack.
“We asked the local community to cooperate with the police … we have received a lot of information, which we are investigating thoroughly," Szymczyk said.
"We value every piece of it,” he added.
In recent weeks, Poland has seen a number of attacks by anti-vaxxer groups on COVID-19 vaccination centres in various locations around the country.
In one such incident, a mobile vaccination site in the southeastern city of Zamość was set ablaze at the start of this month, prompting Polish Health Minister Adam Niedzielski to declare a policy of “zero tolerance for such behaviours.”
Last week, in the central town of Grodzisk Mazowiecki, 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.
Polish Prime Minister Mateusz Morawiecki told reporters earlier this week that some of the assailants in Grodzisk Mazowiecki had made punishable threats and had been detained as a result.
Morawiecki also said that his government would take strict measures against anti-vaxxers.