"I ask you to find Alexei Ulyukayev guilty," prosecutor Boris Neporozhny said in a Moscow court, asking for a 10-year prison sentence and a fine of 500 million rubles ($8.5 million).
"The guilt of the defendant in receiving a bribe is completely proven."
Ulyukayev was arrested last year while still a minister, allegedly caught red-handed in a sting operation to greenlight the acquisition by state oil giant Rosneft of a stake in oil company Bashneft.
Prosecutor Neporozhny accused Ulyukayev, who has spoken out against state intervention in the economy, of extorting $2 million from Rosneft chief Igor Sechin, who is a confidante of Putin, and is considered by many to be the second-most powerful man in Russia.
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Sechin has refused to appear as a witness in the trial despite being summoned repeatedly, citing his busy schedule.
Ulyukayev has denied the charges, saying he has been framed. He says he accepted a basket from Sechin which he thought contained wine and other gifts.
Neporozhny accused the former economy minister of showing Sechin two fingers in an apparent code for $2 million.
The prosecutor insisted that Ulyukayev had extorted the bribe despite not needing anything and "rolling in money."
In Russia, trials almost always end in a conviction.
Ulyukayev's arrest stunned the country's liberal elites, with Putin sacking him as economy minister in the wake of his detention.
Sechin became one of the most influential figures in Russia after building up Rosneft into the world's largest publicly traded oil company.