Wiebe played junior hockey with the Edmonton Poolers from 1930 to 1932. In 1932-33 he played for the senior Edmonton Superiors and the St. Paul Greyhounds besides his debut for the Chicago Blackhawks. He played the 1933-34 season for the Kansas City Greyhounds. From 1934 to 1944 he played exclusively for the Blackhawks. In his 414 NHL games he scored 14 goals and 27 assists.