Pebdani was born and grew up in Texas. Her parents left Iran in the mid 1970s, five years before the Islamic Revolution.
She received her BFA in theatre from Southern Methodist University and is also an alum of the Dell'Arte International School of Physical Theatre in Blue Lake, California. In early 2000s, Pebdani began appearing on television shows such as The Shield, Ugly Betty, and House. From 2005 to 2013, she had the recurring role of Artemis, the foul-mouthed friend of Sweet Dee, in the FX comedy series, It's Always Sunny in Philadelphia.
Following her work in It's Always Sunny in Philadelphia, Pebdani had guest starring roles on How I Met Your Mother, Modern Family, Raising Hope, Garfunkel and Oates, Brooklyn Nine-Nine, Hot in Cleveland, and House of Lies. Her breakthrough role came in 2014, playing the role of Flo Packer in the second season on the Showtime period drama, Masters of Sex. Her character is the owner of a diet pill company for which Virginia Johnson works as a salesperson for part of the season. Then she becomes involved in a table-turning sexual relationship with another reoccurring character Dr. Austin Langham. In 2015, Pebdani joined the cast of Shonda Rhimes' political drama, Scandal as Susan Ross, the new Vice President of the United States.