Anastasiya was born on October 22, 1986. She graduated from the Moscow Art Theatre School (course of I.Zolotovitsky and S. Zemtsova). Being a student, she made her professional stage debut at Moscow Art Theatre of Chekhov in 2006, where she worked until 2010. Anastasiya played in the following performances: «The Golovlyov Family», «Oblomov», « The Humpbacked Horse», «Amadeus», «Boule de suif», «The River with Rapid Current», «Home of the Gentry», «An Ardent Heart», «Never part with the loved ones», «Undine».

Since 2011 Anastasiya is part of the Maly Theatre’s company. The young actress is intensely involved in the repertoire, and plays all range of characters as young as herself and much older, e.g. Manefa in «Enough Stupidity in Every Wise Man» and Shablova, «Late Love» both plays written by Alexander Ostrovsky. Anastasia herself believes that «Ostrovsky's fraudsters are ageless» and prefers «to focus on the details of their personality carefully written out by the genius playwright.» Anastasiya is a character actress who strives to enter imaginatively into the psychology and physical actions of the characters she’s playing. Her playing style can be tremendously grotesque, however, it always fits seamlessly into the general outline of the play.

In addition to working at the Moscow Art Theatre and the Maly Theatre, Dubrovskaya was also involved in Creative Association «DUET», performing roles in the plays «Nyura Chapay» and «Sabinyaninov's Kidnapping».

Anastasia first appeared on screen in 2004, playing Asya in the TV series «Always Say «Always»-2». The actress also actively collaborates and cooperates with Radio of Russia. She participated in Yury Olesha’s «Envy», Aleksandr Kuprin’s «Allez!», «Skomorokh Pamfalon» by Nikolay Leskov, «The Moscow Masquerade» by Pyotr Boborykin.