Elliot Investors' call to remove Antony Burgmans follows the Dutch firm's refusal to enter talks with US rival PPG Industries over a $24bn takeover.
Akzo has rejected two offers from PPG, but some shareholders - including Elliott - support the bid.
Mr Burgmans and chief executive Ton Buechner say the bid undervalues Akzo.
Elliott said it was one of a group of investors that meets the Dutch legal threshold of 10% support needed to call an extraordinary meeting to vote on a proposal to remove Mr Burgmans.
That process takes about two months.
An Akzo Nobel spokesman said the company strongly supported the chairman and would respond to the request within 14 days as required by Dutch law.
"The removal of Mr Burgmans would be irresponsible, disproportionate, damaging and not in the best interest of the company, its shareholders and other stakeholders," he said.
Meanwhile, the company has reported Elliot and PPG to Dutch regulators for possibly sharing potentially "sensitive" information with PPG regarding support for an extraordinary meeting.
It was not clear what rules, if any, the shareholder and PPG might have violated.
Elliott, which has a 3.25% stake in Akzo, said it would respond to the company's allegations soon.
PPG could not be reached for comment.
Elliott, which became an Akzo shareholder in December, is known for its aggressive moves.
Founded in 1977 by American activist investor Paul Singer, it made a name investing in national debt in countries such as Peru. The firm is most famous for its long legal battle over Argentine debt, which climaxed when the firm seized an Argentine naval ship docked in Ghana.
The hedge fund is also pushing mining giant BHP Billiton to reorganise and spin off its US oil unit.
The PPG offer that Akzo rejected on 22 March was worth more than 24bn euros. Akzo shares were flat at 79.12 euros in Amsterdam on Wednesday.
Mr Buchner has proposed selling Akzo's chemicals division and has embarked on a series of share repurchases.
The firm, which is scheduled to meet with investors later this month, has also drawn opposition from Dutch politicians concerned about potential job losses.
An activist investor in Akzo Nobel has increased the pressure on the Dulux paint owner by calling for its chairman to be removed.