Kim, 34, explained that Rob had been in the dark about Caitlyn's photo shoot, and when shown a photo in advance, Rob was unaware that it was their step-father.
Caitlyn, formerly Bruce Jenner, made her public debut on the cover of Vanity Fair, which was unveiled yesterday. The cover follows on from Caitlyn's tell-all interview in April, in which she came out as transgender.
Talking to Access Hollywood at the CDFA Fashion Awards on Monday (1 June), Kim said: "It was so funny because all the girls, we knew that Caitlyn was shooting this but my brother had no idea. So I sent it on a mass text to everyone and my brother was on it and he goes, 'Kim, why are you sending me this? Who is this woman? And why do I care?'
"And I was like, 'Rob, that's Bruce! That's Caitlyn!' And he was like, 'Oh my god, she's beautiful!' And then he called her and they had a lovefest and it was so cute. But the moment was so funny."
Kim, who announced on the latest episode of Keeping Up With The Kardashians that she was pregnant with her second child, said she shared "glam tips" with Caitlyn, telling her to practice and feel comfortable.
Kim added: "She figured it out. She looked amazing."
After the unveiling of the Vanity Fair cover, Caitlyn joined Twitter and received an outpouring of support from family, fellow celebrities and fans.
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