The heads the Khanty-Mansiisk Oil Company and Nazym Oil and Gas Exploration Company were taken into custody on Wednesday.
The two brothers, Alexander and Nikolai Pershin, are directors
of the respective companies operating in the far-eastern region of Siberia.
"They are accused of embezzling more than one and a half billion roubles from the budget for the development of natural resources," Nurgaliyev told the ITAR-TASS news agency.
The minister also said an investigation was under way into allegations concerning the leadership of the Khanty-Mansiisk autonomous region, about 2500km east of Moscow.
He said investigators suspected the scam had caused half a billion roubles ($17.8 million) worth of economic damage to the state by selling 461 oil wells at discounted prices, Interfax reported.
He said his ministry should make it a high priority this year to strip organised criminal groups of "the opportunity to control major sectors of the economy, including the fuel and energy sector, considerable budget assets and export operations".