He played junior and senior hockey in Jonquière, Quebec from 1955 to 1961. From 1961 to 1963 he played for the Amherst Ramblers of the Nova Scotia Senior Hockey League. In 1963-64 he signed with the Montreal Canadiens. Morissette played in 7 games for the Omaha Knights, 5 with the Cleveland Barons, and 1 for the Quebec Aces. On October 30, 1963, he replaced the injured Gump Worsley for the Canadiens in the second period in a game against the Toronto Maple Leafs. Morissette let in 4 goals in a 6-3 loss. Morissette played eight more seasons with minor pro and senior teams and retired in 1972.