Upon making his NHL debut on December 23, 2008, Brett became the eighth member of the Sutter family to play in the NHL. Along with his father, Darryl, his uncles Brent, Brian, Duane, Rich and Ron all played in the NHL, while his cousin Brandon is a member of the Vancouver Canucks. Another cousin, Shaun, was also a draft pick of the Flames in 1998, and later became an assistant coach of the Regina Pats of the Western Hockey League. Two of his other cousins, Brody and Lukas, also played in the Western Hockey League and have been drafted into the NHL.