The footage, filmed in southwestern Poland and aired on news channel TVN24 this weekend, shows a group of men wearing Nazi-inspired uniforms performing Nazi salutes.
Among those caught on camera was a man identified in the report as Mateusz S., the leader of neo-Nazi group Pride and Modernity (DN).
He appears to have been speaking at an event marking 128 years since the birth of Nazi dictator Adolf Hitler, held on a hill near the southwestern Polish village of Wodzislaw on an undisclosed date.
Poland's Internal Security Agency on Tuesday arrested him and two other men identified only as Adam B. and Thomas R. for legal reasons.
A search of their residences turned up Nazi paraphernalia, including uniforms, flags and literature along with an illegal firearm.
They face charges of publicly propagating Nazism for having organised the event which "praised and affirmed this type (Nazi) of government with emblems, recordings and texts as well as other gestures referring to Nazi symbolism," Ewa Bialik, spokeswoman for the national public prosecutor's office, told the Polish PAP news agency.
Totalitarian ideologies like fascism or communism and ethnic or racial hatred are banned in Poland, and carry a penalty of up to two years behind bars.
Poland's deputy justice minister Patryk Jaki on Tuesday asked the national public prosecutor's office to ban the Pride and Modernity group.
'No tolerance'
Undercover journalists also filmed large red flags with Nazi swastikas hanging on trees and an altar with a portrait of Hitler.
Participants in the event set fire to a large wooden swastika soaked in flammable liquid that was fixed to a tree as they played a soundtrack of Nazi military marches.
Referring to the neo-Nazi event, Poland's rightwing Prime Minister Mateusz Morawiecki said Monday on Twitter that "there is no tolerance for these kinds of behaviours and symbols."
World War II erupted when Nazi Germany invaded Poland in September 1939.
Some six million Polish citizens, half of whom were Jewish, perished under the Nazi occupation that lasted until 1945.
In November, leaders of the governing right-wing Law and Justice (PiS) party spoke out against xenophobia after a controversial Independence Day march organised by far-right and nationalist groups that drew 60,000 participants and a chorus of condemnation from around the globe.
While many marchers denied membership of or sympathy for extreme right groups, the event also drew representatives of far-right parties from across Europe.