Camille Henry played his junior hockey for the Citadelles of the Quebec Junior Hockey League. In both 1951-52 and 1952-53, he led the league in total goals with 55 and 46 respectively. In 1951-52, he also led in the total points category with 114 in a 50 game season. These numbers earned him a spot on the QJHL First All-Star team both years. He also made a Memorial Cup appearance with the Citadelles in 1953, and put up 21 points in eight games.
The 1953-54 season also saw Henry making his NHL debut as a New York Rangers, for whom he played 66 games and put 39 points on the board. This rookie year performance won him the Calder Memorial Trophy. He returned for 21 games with the Blueshirts the following season and was then traded to Providence (AHL) and subseqeuntly loaned to Quebec (QHL). He tallied 38 points in 37 games for the Quebec Aces. Providence kept Henry in their own lineup the following season, and he led the AHL in goals with 50. He also added 41 assists for a total of 91 points in 59 games. He capped his AHL season by leading all players in playoff goals with ten in nine games.
In 1956-57, he was divided his time between New York and Providence, notching 29 points in 36 games for the Rangers, and 47 points in 29 games for Providence. After that, it was all NHL for the next seven seasons for Henry. During the 1957-58, he played 70 games for the Rangers, and put up 32 goals and 24 assists for a total of 56 points. These numbers, combined with a style of play that kept him out of the penalty box for all but two minutes the entire season, earned him the 1958 Lady Byng Trophy. He was also voted to the NHL Second All-Star team.
Henry played for the Rangers until February 1965. During his tenure as a Blueshirt, he consistently hit double digits in both goals and assists while spending minimal time in the penalty box. He had an NHL career best during the 1962-63 season when he scored 37 goals and 23 assists for a total of 60 goals in 60 games. He played 48 games for the Rangers during the 1964-65 season before being traded to Chicago as part of multi-player deal. He participated in the NHL All-Star game in both 1963 and 1964.
He played the 1965-66 season for the St. Loius Braves of the CPHL. Henry dabbled with retirement the following season, but 1967-68 saw him back on ice, with both the New York Rangers and the Buffalo Bisons of the AHL. He played his last two seasons with hte St. Louis Blues organization before retiring for good in 1970.