David Einhorn, the head of hedge fund Greenlight Capital, demanded Apple hand investors more of its cash, which makes up nearly a third of its stock market value.
It comes ahead of the company's annual meeting, where Apple's board is likely to be questioned about its falling share price.
Although still the most valuable company in the world, Apple is facing increasing competition in the smartphone and tablet markets from rivals like Samsung.
Its once rapid growth has slowed and its stock has fallen around by 35% in value since its record-high in September.
Mr Einhorn, who filed a lawsuit at the US District Court in Manhattan, is opposed to a move by Apple that would make it more difficult to issue preferred stock.
Currently, the board is able to issue preferred stock but it wants shareholders to vote on a proposal that would require shareholder approval first.
The hedge fund manager, who has a history of criticising companies publicly, urged fellow investors to reject the plan.
"Apple has $145 per share of cash on its balance sheet. As a shareholder, this is your money," Mr Einhorn said in a letter to the company.
In response, Apple said the lawsuit over the proposal was misguided.
"Contrary to Greenlight’s statements, adoption of Proposal #2 would not prevent the issuance of preferred stock," it said in a statement.
The company insisted its management team and board had been in "active discussions" about returning cash to shareholders.
Apple began to be conservative with its cash following its near-collapse in the 1990s, before founder Steve Jobs returned to the company.
It has never explained its reasons for holding onto the cash other than to say its preserving its options.
But analysts expect it to come under further pressure from shareholders at the annual meeting on February 27 to start releasing some more of its money.
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