Baker grew up in Amherst, Mass., and graduated from the Department of Dramatic Writing at New York University's Tisch School of the Arts. She earned her MFA from Brooklyn College.
Her play Body Awareness was staged off-Broadway by the Atlantic Theater Company in May and June 2008. The play featured JoBeth Williams and was nominated for a Drama Desk Award and an Outer Critics Circle Award. Circle Mirror Transformation premiered off-Broadway at Playwrights Horizons in October 2009 and received Obie Awards for Best New American Play and Performance, Ensemble. Her play The Aliens, which premiered off-Broadway at Rattlestick Playwrights Theater in April 2010, was a finalist for the 2010 Susan Smith Blackburn Prize and shared the 2010 Obie Award for Best New American Play with Circle Mirror Transformation.
Baker's adaptation of Anton Chekhov's Uncle Vanya premiered at the Soho Repertory Theatre in June 2012 and was called a "funky, fresh new production" by a New York Times reviewer. Her play The Flick premiered at Playwrights Horizons in March 2013. A New York Times reviewer wrote, "Ms. Baker, one of the freshest and most talented dramatists to emerge Off Broadway in the past decade, writes with tenderness and keen insight." The play received the Obie Award for Playwriting in 2013.
Baker teaches in the MFA program at Stony Brook Southampton. She was one of seven playwrights selected to participate in the 2008 Sundance Institute Theatre Lab. In 2011 she was named a Fellow of United States Artists.