Kim, Kourtney and Khloe Kardashian joined family members including siblings Kylie and Kendall Jenner and Rob Kardashian for the promo, which sees them lip syncing to the song.
Kris and Bruce Jenner also appear, alongside Kim's new fiancé Kris Humphries, Khloe's husband Lamar Odom, and Kourtney's boyfriend Scott Disick and young son Mason.
According to posts on Kim, Khloe and Kourtney's official websites, the video was devised, directed and edited by Kylie and Kendall.
"We all learned the words to Katy Perry's song 'Extraterrestrial' (even Bruce LOL) and then took turns lip syncing to it. My favourite part is where Masey is dancing. How cute is he?! (sic)" wrote Khloe.
"I'm so happy Kenny and Kylie made this video - it's so much fun for us to watch and it's something we'll always have. I love my family!!!!"
Kim said: "I can't believe how great it turned out. [Kylie and Kendall] truly are geniuses!"
"We had so much fun making it… just being silly and fooling around," added Kourtney. "Every time I hear this Katy Perry song I think of my mum's face saying 'You're so hypnotizing'!"
The family can be seen in the new season of Keeping Up With The Kardashians from June 12 at 10/9c on E!
Watch the Kardashians' music video for Katy Perry's 'E.T.' below: