Ulyukayev, 61, was arrested last year while still a minister, allegedly caught red-handed in a sting operation supervised by the FSB security service to greenlight the acquisition by state oil giant Rosneft of a stake in state-run oil company Bashneft.
He is the highest-ranking official arrested during Putin's 17 years in power.
Prosecutor Boris Neporozhny called for a 10-year sentence for the former minister in a "harsh regime" penal colony for extorting a bribe from Rosneft chief Igor Sechin.
"I ask you to find Alexei Ulyukayev guilty," the prosecutor said in a Moscow court as he also called for a fine of 500 million rubles ($8.5 million).
"The guilt of the defendant in receiving a bribe is completely proven," he said, adding that Ulyukayev should be stripped of his state awards.
Neporozhny accused Ulyukayev, who has spoken out against state intervention in the economy, of extorting $2 million from Sechin, who is a confidante of Putin, and is considered by many to be the second-most powerful man in Russia.
Sechin has refused to appear as a witness in the trial despite being summoned repeatedly, citing his busy schedule.
A judge earlier said the court had summoned Sechin by fax, mail and courier.
Ulyukayev insists he has been framed, saying he accepted a hamper from Sechin which he thought contained wine and other gifts.
On Monday, he appealed on the judge to acquit him, saying had been "provoked", and also asked for materials on the role of Sechin and the FSB security service to be passed to investigators.
Ulyukayev's arrest stunned the country's elites, with Putin sacking him from the post he had held since 2013 in the wake of his detention.
Investors are watching the case for signs of Russia's future direction as Putin is widely expected to extend his rule until 2024 in a March vote.
'Rolling in money'
Neporozhny accused the former economy minister of showing Sechin two fingers in an apparent code for $2 million.
According to testimony obtained from Sechin, Ulyukayev flashed a V sign at the Rosneft chief during a pool game at a BRICS summit in India in 2016.
"You personally took the bag with $2 million intended as a bribe," the prosecutor said, adding that the former minister "tried to present himself as a victim of a provocation."
Neporozhny insisted that Ulyukayev had extorted the bribe despite not needing anything and "rolling in money."
Observers say that the pressure against Ulyukayev -- and a tough sentence -- would play out well with the voters ahead of the presidential election, with corruption a top concern for everyday Russians.
Ulyukayev, who has looked gaunt and wan during court appearances, sought to put on a brave face on Monday, saying at the start of the hearing that his mood was "very good."
The former minister appeared calm, reading notes.
In Russia, a judge often sides with the prosecution, with trials almost always ending in a conviction.
Eva Merkacheva, deputy chair of Moscow's Public Monitoring Commission which promotes prisoners' rights, said Ulyukayev may not survive a decade in jail, calling it a veritable "death sentence."
"Ulyukayev, who is under house arrest, has called ambulances several times," she told AFP, adding he had lost weight and suffered from a number of ailments.
"Ten years in a harsh regime colony is basically 20 years in a regular colony," she added.
Ulyukayev's attorney Timofei Gridnev called for his house arrest to be lifted and his money and possessions returned.
He argued that the defendant did not have powers to decide the Bashneft deal.
"All the fateful decisions were taken by the government," he said.
Ulyukayev had originally opposed the sale of the stake in Bashneft to Rosneft but later endorsed it after Putin said it could help fill state coffers.
Sechin became one of the most influential figures in Russia after building up Rosneft into the world's largest publicly traded oil company.
Putin critic Mikhail Khodorkovsky, who spent a decade behind bars, famously accused Sechin of masterminding his persecution.