"We constantly strive to stage work of the highest caliber, and I'm obviously thrilled that our productions have been recognized with so many nominations," Artistic Director Michael Grandage said in a statement.
Four out of the six Donmar Warehouse productions staged in the last year have been recognized, with the current production of "Othello" securing four nominations and Rob Ashford's production of the musical "Parade" nabbing seven.
The nominations for "Othello" include a Best Actor nod for Chiwetel Ejiofor and a Best Actress nomination for Kelly Reilly.
Michelle Fairley was also nominated for Best Actress in a Supporting Role and Tom Hiddleston shortlisted for Best Newcomer for their work in "Othello."
Ashford earned nominations for Best Choreographer and Best Director for "Parade."
"Parade," which will compete for the Best New Musical title, also garnered nods for Lara Pulver in the Best Actress in a Musical category and for Bertie Carvel in the Best Actor in a Musical race.
Penelope Wilton is nominated for the Best Actress prize for her performance in "John Gabriel Borkman" and Michael Frayn's "The Crimson Hotel" is in the running for Best New Comedy.