Arnault's departure comes as Vivendi chief executive Jean-Marie Messier faces calls from investors for his resignation over his handling of the company's financial situation.
In the last week, it has emerged that Messier is placing 15.6% of Vivendi's environmental division, which owns UK train operator Connex, with Deutche Bank, freeing up €1.7bn in cash for the media company.
However, despite raising desperately needed cash for the group, Messier has come under fire for not waiting for better market conditions.
Yesterday, it also emerged that Vivendi's proposed sale of its Italian pay-TV company to News Corporation was in jeopardy because News Corp chairman Rupert Murdoch had failed to find financial backers to support his Italian plans.
Arnault is the fourth board member to resign from Vivendi since March. He follows Rene Thomas, honorary chairman of BNP Paribas; Jean-Louis Beffa, CEO of Saint-Gobain; and Phillippe Foriel-Destezed, a former Adecco CEO.
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