The ministry said the film's release was cancelled after officials found it contained "information whose distribution is legally banned in Russia".
The Anglo-French film was set for a limited release in cinemas from Thursday after local distributors Volga Film gained an 18+ certificate from the culture ministry.
This prompted a wave of protests from conservative figures, although it received good reviews in Russian broadsheets.
On Monday, Culture Minister Vladimir Medinsky held a private screening for officials and film directors.
Yelena Drapeko, deputy head of the lower house of parliament's culture committee, told the RBK news site that she had "never seen anything so disgusting in my life".
"(The audience), me included, saw elements of extremism in the film," she said.
After the screening 22 people signed a letter urging Medinsky to delay the release and check if the film broke any laws.
The signatories included film director Nikita Mikhalkov -- who won an Oscar for his 1995 film "Burnt by the Sun" set during Stalin repressions -- and Marshal Zhukov's daughter Era.
The letter published on the culture ministry's site slammed the film as "lampooning the history of our country" and "blackening the memory of our citizens who conquered fascism".
The film contained elements "that can be assessed as extremist and aimed at humiliating Russian people," the letter said.
The Russian national anthem was used in an "offensive way" in the trailer, it added.
It also called for the release to be delayed because next month sees the 75th anniversary of Soviet victory against the Nazis in the Battle of Stalingrad in 1943.
One of the letter's signatories, the head of a public chamber advising the culture ministry, Yury Polyakov, told TASS state news agency the film is "part of an ideological battle against our country".
Kremlin spokesman Dmitry Peskov told journalists earlier Tuesday that he was not aware of the controversy and that the matter was the prerogative of the culture ministry.
"The Death of Stalin" became the top trending item on Russian Twitter after the announcement.
"I think Charlie Chaplin would be under house arrest now in Russia," wrote Alexei Venediktov, editor-in-chief of popular Echo of Moscow radio.
The film has prompted a mixed reaction from Russian media, ranging from praise to condemnation.
The Komsomolskaya Pravda tabloid slammed it as "a comedy that could have been filmed by Hitler" and "possibly the most sickening film about the USSR of recent times".
But critic Andrei Arkhangelsky wrote in Ogonyok magazine that the irreverent comedy is paradoxically able to "convey the full seriousness of what happened".