Greek shipping magnate Marinakis filed the case at the High Court against CPFC Limited and "Persons Unknown". The Lawyer reported that the case related to a provocative banner held by Palace supporters at the home game against Forest last August.
Marinakis was the target of Palace fans' ire after the London side were demoted from that season's Europa League to the Conference League for breaching UEFA multi-club ownership rules, with Forest taking their place in the second-tier competition.
The banner showed Marinakis holding what appeared to be a gun to the head of midfielder Morgan Gibbs-White, with a speech bubble which read: "Mr Marinakis is not involved in blackmail, match-fixing, drug trafficking or corruption."
Marinakis, who acquired Nottingham Forest in 2017 and also owns Greek side Olympiacos, has repeatedly denied allegations involving match-fixing, corruption and other illicit activities.
His lawyers and Palace did not immediately respond to a request for comment on the lawsuit filed on Monday.