The departure of Mack, aged 69, after less than a year on the board, comes after the United States imposed sanctions on Rosneft's head Igor Sechin over Russia's actions in Ukraine.
Rosneft said his decision to leave was not connected to the sanctions.
"He left for personal reasons," a spokesman for Rosneft said.
Rosneft also said that Artur Chilingarov, 74, has been proposed to replace Mack on the board. Chilingarov, a member of Russia's upper house of the parliament, is known for his exploration of the Arctic, seen as an important source for Rosneft's future hydrocarbon production.
He joined Rosneft's board last June after Rosneft bought Anglo-Russian oil firm TNK-BP for $55 billion from BP and the AAR consortium.
Six months later Rosneft announced it would buy the majority of the global physical oil trading operations of Morgan Stanley.
Rosneft has said that the deal with Morgan Stanley is intact and will be completed in the second half of this year.