When asked if it was fun for the duo, Malek said, "I don't know that it was".
"I've known her for many years, despite as it may seem from that video", the 37-year-old said with a laugh.
It won best musical or comedy film, best screenplay and best supporting actor for Mahershala Ali. The Mexican movie, which also took the prize for best director, is seen as an Oscar frontrunner in February.
As fans chimed in to "like" the photo and express their love of the movie as well, one cheeky woman wrote, "Sir Rod - when do we get a film about you?"
Rami Malek is being "haunted" by his on-stage snub from Nicole Kidman at the Golden Globes.
It beat out "Vice", the polarizing Dick Cheney biopic, which led all films with six nominations.
"This is beyond anything we ever imagined when we began shooting", said director and writer Peter Farrelly.
Set in the 1960s and co-starring Viggo Mortensen, Green Book tells the story of an African-American musician who hires an Italian-American driver to take him on a tour of the Deep South. From The Star is Born's Lady Gaga to the gorgeous cast of Black Panther, our favourite Hollywood stars slayed it with their bold fashion choices. "So I thought I could easily go up and say hi". "Right now this moment is real. I am privileged to be counted among you". "And now so will everyone else".
He first tried to speak to her, but she didn't notice him.
But while the film has found itself the talk of numerous awards ceremonies already, and recently scored a huge night at the Golden Globes, it hasn't fared too well with critics.
Malek was competing against Bradley Cooper (A Star Is Born), Willem Dafoe (At Eternity's Gate), Lucas Hedges (Boy Erased), and John David Washington (BlacKkKlansman) in the category.
British actress Olivia Coleman was a victor for bawdy historical romp "The Favourite".