Marinakis' lawyers lodged the claim in the High Court on Monday, with CPFC Limited named as one of two defendants.
The banner, displayed by supporters in the Holmesdale Road End during a 1-1 Premier League draw between the two clubs at Selhurst Park last August, read: "Mr Marinakis is not involved in blackmail, match-fixing, drug trafficking or corruption."
Marinakis, a Greek shipping magnate who has owned Nottingham Forest since 2017, has consistently and vehemently denied any wrongdoing in relation to such allegations.
Crystal Palace were fined £50,000 by the Football Association in February after initially denying a charge of failing to ensure their supporters did not behave in an improper, offensive, abusive or provocative way, with the FA noting that the club's own policy to prevent banners being smuggled into the stadium demonstrated it had been aware of the risk.
While the banner itself was not specified as the reason for that charge, strict rules govern messaging deemed defamatory, political or offensive.
The banner referenced England international Morgan Gibbs-White's sudden U-turn over a proposed transfer to Tottenham the previous summer, after Spurs appeared to trigger a £60m release clause in his contract before he signed a new deal to stay at Forest, discussing his decision in an interview alongside Marinakis.
The display came amid deep tension between the two clubs, which had gone head to head over a place in last season's Europa League after Uefa ruled Forest would take Palace's spot due to the south London club's breach of multi-club ownership rules involving former co-owner John Textor's stake in Lyon.
Palace, demoted to the Conference League as a result, went on to win the competition for their first major European trophy. In a further twist, Palace's title-winning manager Oliver Glasner departed at the end of last season and has since taken charge of Forest, meaning he will now work directly for Marinakis, with the two clubs due to meet again at Selhurst Park in October.