After playing three seasons (1931-34) in the Manitoba Junior Hockey League with the Winnipeg Columbus Club and Selkirk, Shibicky signed with the New York Rangers. He played one season with the Brooklyn Crescents and one with the Philadelphia Ramblers and then made it to the Rangers in 1936-37. Shibicky played six seasons for them, winning the Stanley Cup in 1939-40. Shibicky joined the Canadian Army in 1942 for World War II. He played for the Allan Cup-winning Ottawa Commandos in 1942-43. Shibicky played in 324 NHL games, scoring 110 goals and 91 assists.