In a letter distributed by Yukos, Steven Theede, an American, refers to the controversial 2004 auction of Yukos's production unit, Yuganskneftegaz, which was eventually acquired by state-controlled Rosneft.
This week saw shares of Rosneft begin trading on the London Stock Exchange, a move Yukos had opposed.
Rosneft hopes to make $10.4 billion through the flotation.
Theede's resignation comes before a meeting of creditors today, which was expected to lead to the company's liquidation. Theede said he wanted no part in the meeting as he did not want to be associated with a "charade."