Waller-Bridge's show "Fleabag" is up for the Noel Coward Award for Best Entertainment or Comedy Play award, while she is nominated for Best Actress for her performance as the title character.
In the Best Actress section she is up against Hayley Atwell ("Rosmersholm"), Sharon D. Clarke ("Death of a Salesman") and Juliet Stevenson ("The Doctor").
McAvoy ("Cyrano de Bergerac") and Pierce ("Death of a Salesman") are nominated for the Best Actor prize. The other nominees are Toby Jones ("Uncle Vanya") and Andrew Scott, who starred in the TV version of "Fleabag", for Present Laughter.
Andy Nyman ("Fiddler on the Roof"), Charlie Stemp ("Mary Poppins"), Sam Tutty ("Dear Evan Hansen") and Jac Yarrow ("Joseph and the Technicolor Dreamcoat") are up for Best Actor in a Musical.
Those up for Best Actress in a Musical are Audrey Brisson ("Amelie The Musical"), Judy Kuhn ("Fiddler on the Roof"), Miriam-Teak Lee ("& Juliet") and Zizi Strallen ("Mary Poppins").
Another notable nominee is Petula Clark, last Olivier-nominated in 1981, who receives a nod for Best Supporting Actress in a Musical for her role as the Bird Woman in "Mary Poppins".
The William Shakespeare inspired musical "& Juliet" leads with the most nominations, with nine, including Best New Musical. The awards will be handed out in a ceremony at London's Royal Albert Hall on 5 April, with British comedian Jason Manford hosting.
The full list of nominees is as follows:
Best Actor in a Supporting Role in a Musical:
David Bedella for "& Juliet" at Shaftesbury Theatre
Stewart Clarke for "Fiddler on the Roof" at Playhouse Theatre
Jack Loxton for "Dear Evan Hansen" at Noel Coward Theatre
Rupert Young for "Dear Evan Hansen" at Noel Coward Theatre
Best Actress in a Supporting Role in a Musical:
Lucy Anderson for "Dear Evan Hansen" at Noel Coward Theatre
Petula Clark for "Mary Poppins" at Prince Edward Theatre
Cassidy Janson for "& Juliet" at Shaftesbury Theatre
Lauren Ward for "Dear Evan Hansen" at Noel Coward Theatre
Best Original Score or New Orchestrations:
"& Juliet" - New Orchestrations by Bill Sherman and Dominic Fallacaro at Shaftesbury Theatre
"Amelie the Musical" - Musical Supervisor and Arrangements by Barnaby Race at The Other Palace
"Dear Evan Hansen" - Music and Lyrics by Benj Pasek and Justin Paul, Orchestration by Alex Lacamoire at Noel Coward Theatre
"Fiddler on the Roof" - New Orchestrations by Jason Carr at Playhouse Theatre
"Waitress" - Music and Lyrics by Sara Bareilles at Adelphi Theatre
Best New Dance Production:
"La Fiesta" by Israel Galvan at Sadler's Wells
"Ingoma" by Mthuthuzeli November for Ballet Black at Royal Opera House - Linbury Theatre
"MAM" by Michael Keegan-Dolan for Teac Daṁsa at Sadler's Wells
"Vessel" by Damien Jalet & Kohei Nawa at Sadler's Wells
Outstanding Achievement in Dance:
Sara Baras for her choreography and performance in Ballet Flamenco - Sombras at Sadler's Wells
Anne Teresa De Keersmaeker for her performance in Mitten Wir Im Leben Sind/Bach6Cellosuiten at Sadler's Wells
Gisele Vienne for her choreography of Crowd, presented by Dance Umbrella at Sadler's Wells
Noel Coward Award for Best Entertainment or Comedy Play:
"Emilia" at Vaudeville Theatre
"Fleabag" at Wyndham's Theatre
"Magic Goes Wrong" at Vaudeville Theatre
"The Upstart" Crow at Gielgud Theatre
Best Theatre Choreographer:
Fabian Aloise for "Evita" at Regent's Park Open Air Theatre
Matthew Bourne and Stephen Mear for "Mary Poppins" at Prince Edward Theatre
Jerome Robbins and Matt Cole for "Fiddler on the Roof" at Playhouse Theatre
Jennifer Weber for "& Juliet" at Shaftesbury Theatre