It will compete with Come From Away, Dear Evan Hansen and Groundhog Day for the top prize.
Following close behind is the revival of Hello Dolly! with 10 nods and Dear Evan Hansen with nine.
Up for Best Play are A Doll's House, Part 2, Oslo, Indecent and Sweat.
Shortlisted for Best Revival of a Play is August Wilson's Jitney, Lillian Hellman's The Little Foxes, Present Laughter and Six Degrees of Separation.
In the running for Best Revival of a Musical are Falsettos, Hello, Dolly! and Miss Saigon.
Among the actors and actresses nominated for Tonys this year include Cate Blanchett for The Present; Sally Field for The Glass Menagerie; Andy Karl for Groundhog Day; Chris Cooper, Condola Rashad and Laurie Metcalf for A Doll's House, Part 2; Corey Hawkins for Six Degrees of Separation; Kevin Kline for Present Laughter; Jefferson Mays and Jennifer Ehle for Oslo; Ben Platt and Mike Faist for Dear Evan Hansen; Laura Linney, Cynthia Nixon and Richard Thomas for Little Foxes; Christian Borle, Stephanie J. Block and Andrew Rannells for Falsettos; Christine Ebersole and Patti LuPone for War Paint; Danny DeVito for Arthur Miller's The Price; and Bette Midler, Gavin Creel, Kate Baldwin and David Hyde Pierce for Hello, Dolly!
Kevin Spacey is to host the June 11 Tonys ceremony honoring excellence on Broadway. The gala will air on CBS.