Apple’s cash pile has grown to that size from $98bn last March.
US hedge fund manager, David Einhorn, who is behind the unusual move, told the television channel CNBC that Apple had a “Depression-era” mentality, which gave it a tendency to hoard cash and play safe.
Apple called the move “misguided”.
The complaint was filed at a court in New York.
Apple has a number of fights on its hands already. Although it is strong in both smartphones and tablet computers, competition is hotting up and its share price is falling.
The firm’s shares are now 35% below the record high they reached in September 2012.
Mr Einhorn, who owns Green Light Capital, told CNBC: “It has sort of a mentality of a depression. In other words, people who have gone through traumas… and Apple has gone through a couple of traumas in its history, they sometimes feel like they can never have enough cash.”
He has also been speaking to the Reuters news agency, which he told he had had meetings with Apple’s senior management on the subject of sharing out the cash pile.
Mr Einhorn said he had recently contacted Apple’s chief executive, Tim Cook after failing to interest the company’s chief financial officer, Peter Oppenheimer, in the matter.
Mr Einhorn’s proposals for releasing funds to shareholders involve “preferred” stock – which pays a fixed dividend over time.
Apple is planning to eliminate these at its shareholder meeting later this month.
Preferred shares rank higher than ordinary shares when it comes to paying out a company’s assets.
Mr Einhorn has a history of activism.
In 2011, he urged Microsoft Corp to get rid of its chief executive Steve Ballmer, accusing him of being “stuck in the past”.