Kaplan was born to an Orthodox Jewish family in Manhattan, the son of Tobias D. Kaplan, a successful shirt manufacturer in New York City, and Anna (Rudman) Kaplan, a homemaker. Both of his parents died by the time he was nine. "I spent a lot of time as a boy playing in Central Park and walking around Manhattan by myself," he recalled in a 1981 Boston Globe interview. He was raised by an older brother and the family's West Indian housekeeper, who taught him to cook, which later came in handy when his wife Anne Bernays turned out to be a self-described "domestic illiterate".