It comes after local media reported that a central Moscow cinema had screened the film, which satirises the death of the dictator, despite the ban.
The ministry withdrew permission for the film's release on Tuesday after Russian officials and arts figures labelled it offensive and "extremist."
In a statement, the ministry said it "reminds" cinemas that according to Russian state law on cinematography, showing a film without permission for release "entails responsibility in accordance to the law".
The ministry said the film's release was cancelled after officials found it contained "information whose distribution is legally banned in Russia".
More From This Section
The 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.
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.