Russia’s main anti-corruption body, the Investigative Committee (SK), said he received a payment of $2m (£1.6m).
Mr Ulyukayev is the highest-ranking Russian official held since the 1991 coup attempt in what was then the USSR.
The SK said he had “threatened” to create obstacles for Rosneft’s operations when it took a 50% stake in another state oil company, Bashneft.
The minister pleaded not guilty to the bribe charge and saw his arrest as “an act of provocation against a state official”, his lawyer said.
According to SK spokeswoman Svetlana Petrenko, “Ulyukayev was caught red-handed”, receiving a $2m bribe on 14 November for giving a favourable assessment of the Rosneft deal. Investigators asked the court to place him under house arrest, Interfax reported.
Mr Ulyukayev’s deputy Yevgeny Yelin was appointed later on Tuesday as acting economy minister.
A ‘strange’ arrest
The apparent sting operation came after months of electronic surveillance, including phone-tapping, officials said. Unconfirmed reports said the internal FSB security service had run the entire operation.