James Franco's survival story, "127 Hours" and the Mark Wahlberg's boxing saga, "The Fighter" were also among the best-picture nominees.
Other best-picture noms included the sci-fi smash "Inception," the British monarchy tale "The King's Speech," the Facebook chronicle "The Social Network," the heist thriller "The Town," the animated blockbuster "Toy Story 3," the Western "True Grit" and the Ozarks crime yarn "Winter's Bone."
Just behind "Black Swan," "The King's Speech" and "True Grit" came in second with 11 nominations apiece.
The 16th annual awards will be handed out Jan. 14 at the Hollywood Palladium in L.A. VH1 will air the show live.
The Critics' Choice nominations are part of a flurry of film honors that will help sort out contenders for the Feb. 27 Academy Awards, whose nominations will be announced Jan. 25.
The Associated Press contributed to this report.