Tatu, who shot to the top of the charts on Sunday with their debut single "All the Things She Said", have sparked fury in the media over accusations they promote "paedo-pop" and target the "dirty old man market".
Their video features Julia Volkova, 18, and Lena Katina, 17, wearing school uniforms, kissing and cuddling.
The BBC said it would be inappropriate to show the video on "Top of the Pops" on Friday because it attracts a young audience.
New footage of the band, whose name translates as "This Girl Loves That Girl", will be shown instead.
"It would be more sensible for us to show something that's exclusive and not controversial," a BBC spokeswoman said.
The BBC move follows a decision by rival ITV1 not to show the video on its Saturday morning music show "CD:UK".
British daytime television hosts, husband and wife team Richard and Judy, have tried to get Tatu's single banned, describing their antics as "paedophile porn".
Ivan Shapovalov, the man behind Tatu, has admitted to various media that he came up with the idea after visiting pornographic websites.
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