In 1961-62, 16-year-old Hank Monteith played for his hometown Stratford Cullitons in Junior B before enrolling at the University of Toronto where he had five years of playing eligibility with the Varsity Blues. In his last two years in 1966 and 1967 the school won the national championship. He graduated with a degree in Commerce.
Fresh out of school Monteith signed a free-agent contract with the Detroit Red Wings. He was sent to play with the Fort Worth Wings of the CPHL. He was called up for 34 games in the Motor City in his rookie year in 1968-69. Over the next few years his seasons were split between Detroit and Fort Worth.
Monteith's last year in the NHL was 1970-71. In all, he appeared in 77 games and had 17 points. He continued to play semi-pro hockey for another four years in OHA Senior A, first with the Oakville Oaks and then the Orillia Terriers.
In 1997 Monteith was inducted to the University of Toronto's Sports Hall of Fame. His older brother Stephen, who also played with the Blues in the early 1960s, was enshrined in 1991. The brothers have donated the Monteith Trophy for annual presentation to the Blues' leading scorer.