Anna Baryshnikov began acting at age 6 in a children's theater production of A Midsummer Night's Dream, portraying Peaseblossom, a handmaiden to fairy queen Titania. After graduating from Northwestern University in 2014, she began acting professionally on various television series, including Doll & Em on HBO. Her parents were initially hesitant about her career choice before becoming supportive. 

Baryshnikov's most prominent role to date was in the 2016 critically acclaimed drama Manchester by the Sea, alongside Casey Affleck and Michelle Williams. Her character, Sandy, is a girlfriend of Patrick Chandler, portrayed by Lucas Hedges. She practiced her character's Boston accent by working with a dialect coach and going to Boston-area malls to hear how local teenage girls really spoke. 

She starred as grad student Maya in the CBS series Superior Donuts, based on the play of the same name by Tracy Letts. The series, which debuted in February 2017, was renewed for a second season by CBS, but Baryshnikov's character does not appear in the second season, with Maya having completed her thesis towards the end of Season 1.

In 2017, she appeared in the Broadway production of the play Time and the Conways.

In 2018, she appeared in drama film The Kindergarten Teacher.

 On September 26, 2018, Baryshnikov was cast in the lead role of Lavinia Norcross Dickinson in Apple TV+ series Dickinson, alongside Hailee Steinfeld.