Bencic was born in Flawil in northeastern Switzerland to Dana and Ivan Benčič. Her parents were both born in Czechoslovakia, but her father's family emigrated to Switzerland in 1968 to flee the Warsaw Pact invasion by the Soviet Union. Her father was a professional hockey player in the Swiss National League A and National League B before becoming an insurance broker. Her mother was a high-level handball player. Bencic hit her first tennis balls at the age of two and began training with her father, who was also a recreational tennis player, for one hour per day at the age of four. She entered her first national tournament at that age, losing to an opponent six years older in straight sets without winning a game. Bencic would regularly face much older opponents as a child and was encouraged by her father to try to win two games per set.