Singer has always been a controversial figure in the movie industry with a history of disruptive on-set behaviour, including on Bohemian Rhapsody, from which he was sacked and was replaced by Dexter Fletcher who completed the shoot.
Rami, who starred as Freddie Mercury in the film, walked up on stage with the rest of the cast when he went to give Nicole a hug just as she turned her back on him.
"What an honour. Thank you", he captioned the image after the Sunday night ceremony.
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One year ago at the 2018 Golden Globes, the words of the night were Time's Up.
The "Mr. Robot" actor also said that he believes Mercury, who was born Farrokh Bulsara, would have been proud of the film if he saw it today.
"So the fact that I knew Nicole [was there], I was like, 'Oh, here's a bit of safety, '" he continued. "Thank you to Freddie Mercury for giving me the joy of a lifetime", he said, adding in a seemingly ad-libbed moment: "I love you, you lovely man".
In an upset, "Bohemian Rhapsody", the biopic about Freddie Mer- cury and British rock band Queen, won best drama.
The director was sacked from the Freddie Mercury biopic in December 2017 a couple of weeks before filming wrapped, amid rumoured tension with Malek, 37, and other members of the cast.
Meanwhile, Richard Madden, star of Bodyguard, thanked his parents for coming all the way from Scotland to see him pick up the same award in the male category.