Matthew was the fourth round, 84th overall selection of the Buffalo Sabres in the 1992 NHL Entry Draft, Barnaby is a graduate of the QMJHL.
In his first full season in the NHL, with the Buffalo Sabres, Barnaby led the league with 335 minutes in penalties. Barnaby also played for Tampa Bay Lightning, New York Rangers, Colorado Avalanche, Chicago Blackhawks and the Dallas Stars. Everywhere he went Barnaby became a fan favorite with his feisty play and give all attitude. Unfortunately, his career was cut short due to concussion issues. He would finished with 834 games played and over 2500 penalty minutes.