The shipping and media magnate is allegedly seen in footage clashing with a prominent member of Prime Minister Kyriakos Mitsotakis' family in the VIP stands during the final between Olympiacos Piraeus and Real Madrid in Athens.
In the footage, Marinakis allegedly slaps Mitsotakis' nephew Grigoris Dimitriadis, who hits back with a punch, before they are pulled apart.
Part of the magnate's t-shirt is ripped in the fracas.
Sports prosecutor Aristides Koreas is looking into whether to charge both men over the incident, ERT said.
A former close aide to the prime minister, Dimitriadis was forced to resign in 2022 over a wiretapping scandal that rocked the government.
Newspapers owned by Marinakis have been critical of his role in the affair.
Marinakis, 58, also owns the Olympiacos Piraeus and Rio Ave football clubs.
He is among dozens of defendants put on trial over the killing of a Greek riot police officer by alleged Olympiacos hooligans in 2023.
He has denied wrongdoing.
Olympiacos have hit out at the prosecution as "unjust collective targeting of our fans" and "fuelled by specific political and business interests".