Shenkman was born to Jewish parents in New York City, Katherine (nee Ruben; an associate at a law firm) and Shepard A. Sheinkman (who worked for a consulting company). Shenkman graduated from Brown University with a B.A. in Philosophy in 1990. He later earned his MFA (Masters of Fine Arts degree) in 1993 from the New York University Graduate Acting Program at the Tisch School of the Arts. His sister, Elizabeth, is married to British publisher Jamie Byng.