The company, which Stan Lee himself is no longer associated with, claims the entertainment giant does not own the rights to the Marvel Comics characters depicted in its films.
SLM maintains that Stan Lee signed over the rights to the superheroes and villains he created to its corporate predecessor in a deal dating back to 1998.
The company says that an amended version of the agreement in question was filed with the US Securities and Exchange Commission in March 2000, almost a decade before Disney acquired Marvel Entertainment.
Marvel has described the lawsuit as "completely frivolous", pointing out that many of the issues involved have already been addressed, The Hollywood Reporter understands.
SLM is seeking $5.5 billion in damages, an amount calculated based on the profits from movies such as The Avengers and X-Men: First Class, as well as the Broadway musical Spider-Man: Turn Off the Dark.