Dratch was born in Lexington, Massachusetts, the daughter of Elaine, a transportation director, and Paul Dratch, a radiologist. Her younger brother, Daniel, is a television producer and writer who has worked most recently on Monk. Dratch grew up the "class clown type", attending William Diamond Middle School and Lexington High School in Massachusetts. Dratch attended the National Theater Institute in the fall of 1986 and graduated from Dartmouth College in 1988, where she majored in drama and psychology and was a member of the improvisational comedy group Said and Done.