Potanin's Interros holds a 30% stake in Norilsk Nickel.
Another Russian billionaire, UC RusAl's co-owner Oleg Deripaska, also said neither he nor Mikhail Prokhorov, president of Onexim Group, would be board members.
Deripaska also said the merger of Norilsk Nickel and aluminum giant RusAl had been delayed indefinitely, but that the Russian government has no plans to nationalize Norilsk Nickel.
RusAl earlier secured a $4.5 billion state loan to refinance a loan obtained in April from a Western banking syndicate for the purchase of 25% plus two shares in Norilsk Nickel from Onexim. The stake was pledged as collateral for the loan from national development bank VEB.
Norilsk Nickel is Russia's largest diversified mining and metals company, the world's largest producer of nickel and palladium, and one of the world's largest producers of platinum, rhodium, copper and cobalt.