Along with Colman Domingo, Jeffrey Wright, Bradley Cooper, and Paul Giamatti, Murphy was nominated for best actor.
The epic biopic about theoretical physicist J Robert Oppenheimer, who is regarded as the father of the atomic bomb, gave the Cork actor the nomination.
During the 96th Academy Awards, Emily Blunt, his co-star, was also recognised in the best supporting actress category.
Competition for her role as a cook in The Holdovers comes from US actress Da'Vine Joy Randolph, who has received numerous precursor awards, including Danielle Brooks for The Colour Purple, Jodie Foster for Nyad, and America Ferrera for Barbie.
In addition, Oppenheimer star Robert Downey Jr. has received an Oscar nomination for best supporting actor for his portrayal of Atomic Energy Commission chairman Lewis Strauss.
Other nominations are Sterling K. Brown for American Fiction, which is about a disgruntled novelist who writes a book that thrusts him into the middle of the hypocrisy he despises, Robert De Niro for Killers Of The Flower Moon, Ryan Gosling for Barbie, Mark Ruffalo for Poor Things, and so on.
The box office smash Barbie has Greta Gerwig, her husband, and co-writer Noah Baumbach nominated in the adapted screenplay category, along with screenwriter Tony McNamara for Poor Things, which is based on Scottish author Alasdair Gray's 1992 novel.
In advance of Jimmy Kimmel's annual presentation, Atlanta star Zazie Beetz and actor Jack Quaid of The Boys unveiled the 96th Academy Awards nominations on Tuesday.
On March 11, the Academy Awards event will begin airing at midnight.
For co-producing Emma Stone's film Poor Things, Irish production company Element Pictures was nominated nine times.