Schultz had played for the British Columbia Hockey League's Westside Warriors for two complete seasons prior to going professional. In 2008-09, Schultz committed to the University of Wisconsin, an NCAA school, after recording 15 goals and 50 points in 49 games. In 121 regular-season games during his three seasons with the Badgers, Schultz recorded 40 goals and 73 assists for 113 points.
Additionally, Schultz participated in 81 Stanley Cup Playoff games, tallying 42 points with 10 goals and 32 assists. The right-handed defender contributed four goals and nine assists for 13 points in 21 games during the Penguins' 2017 Stanley Cup run, which helped them win their second consecutive title.