Bradley Cooper is also nominated for his direction of and performance in the musical remake.
Olivia Colman is also up for a best actress award for The Favourite, for which Rachel Weisz and Emma Stone are also recognised.
Rosamund Pike is nominated for best actress in a film drama, alongside Lady Gaga, for her role in A Private War.
Colman, meanwhile, will compete for the best actress in a film musical or comedy award with Emily Blunt, shortlisted for playing the title role in Mary Poppins Returns.
Blunt said she was "blown away and over the moon" to receive her sixth Golden Globe nomination, adding that she was "delighted in playing every aspect of this extraordinary and iconic character."
"The entire experience working on it was spellbinding and that's largely to do with the incomparable [director] Rob Marshall who took on this project with great love, depth and courage in his heart."
Weisz also expressed gratitude, saying she was "proud to be nominated alongside such a brilliant group of actresses, including my incredible co-star Emma".
"And all hail our nominated Queen Olivia!" she continued. "These honours are a testament to the brilliance of our director Yorgos Lanthimos."