Breen was drafted by the Green Bay Packers in the fifteenth round of the 1963 NFL Draft and played with the team during the 1964 NFL season. He had also been drafted in the sixteenth round of the 1963 AFL Draft by the San Diego Chargers. Following his time with the Packers, he played two seasons with the Pittsburgh Steelers and two seasons with the Los Angeles Rams. 
He played defensive line at the collegiate level for Virginia Tech and was awarded All Southern Conference honors. He also wrestled at Virginia Tech, where he won the Southern Conference Championship at Heavyweight division. Breen was elected to the Virginia Tech Sports Hall of Fame in 2004.