The court in filmmaker Pavel Talankin's home region issued the ruling following an administrative lawsuit, according to local news reporting from the courtroom on Thursday.
The court reportedly found the film contains elements of "extremist symbolism" and "propaganda for terrorism".
It also cited the inclusion of minors whose parents had not consented to their appearance in the film.
As a result, the court ordered a ban on the screening and distribution of the documentary, which has been available on various online platforms in Russia.
Prosecutors argued the film promotes a negative view of the Russian leadership and of the war in Ukraine. Outside Russia, the documentary remains accessible.
Talankin, a teacher and video co-ordinator at a school in the town of Karabash in the Chelyabinsk region, had filmed patriotic school events and interviewed students, documenting what he portrays as the growing militarisation of daily life for children.
He later fled Russia with the footage, which captures social changes following Russia's invasion of Ukraine.
The material was edited into a feature-length documentary by US-based director David Borenstein, who lives in Copenhagen.
The film also traces Talankin's evolution into a vocal critic of the war.
Talankin has since been widely denounced in Russia. Prominent director Nikita Mikhalkov, who won an Oscar in 1995 for Burnt by the Sun, has criticised the documentary as an "outrageous manifesto of hatred towards Russians".
He described it as an anti-Russian production backed by Western broadcasters, including Denmark's DR, the UK's BBC and Germany's ZDF.
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