The TV channel, the content of which is also available on NOW TV, is including the disclaimer with films such as Gone with the Wind, Flash Gordon and Dumbo.
Sky Cinema are adding warnings to select films that contain “outdated attitudes, language and cultural depictions which may cause offence today”.
The move follows the announcement that US streaming service HBO Max was temporarily removing Gone with the Wind amid criticism of its racist depictions of slavery.
A spokesman for Sky told PA: “Sky is committed to supporting anti-racism and improving diversity and inclusion both on and off screen.