Wasserstein was born in Brooklyn New York to Morris Wasserstein, a wealthy textile executive, and his wife, Lola (née Liska) Schleifer, an amateur dancer who moved to the United States from Poland when her father was accused of being a spy. Lola Wasserstein reportedly inspired some of her daughter's characters. Wendy was one of five siblings, including brother Bruce Wasserstein, a well-known investment banker. Her maternal grandfather was Simon Schleifer, a yeshiva teacher in Wloclawek, Poland, who moved to Paterson, New Jersey and became a Hebrew school principal. Claims that Schleifer was a playwright are probably apocryphal, as contemporaries didn't recall this and the assertion only appeared once Wasserstein had won the Pulitzer Prize for Drama
