Schultz played collegiate hockey in the NCAA for the University of Wisconsin, which competed in the Western Collegiate Hockey Association. He played in 121 games and scored 40 goals and 73 assists. Drafted by the Anaheim Ducks in 2008, Schultz was unable to come to terms on a contract with the team. During the last week of May 2012, Schultz officially "de-registered" from the University of Wisconsin triggering a process that made him an unrestricted free agent. According to league rules, from the time Anaheim was given notice of the de-registration from school, they had a 30-day exclusive window to try to sign him or trade him. Anaheim was ultimately unable to sign him. Schultz was heavily recruited by up to 26 teams as a free agent, with the Edmonton Oilers having Wayne Gretzky and Paul Coffey personally recruit him. On June 30, 2012, Schultz agreed to a two-year, entry-level contract with the Oilers. Due to the 2012–13 NHL lockout that cancelled the first three months of the 2012–13 NHL season, Schultz played the first 34 games of his professional career in the American Hockey League for the Oilers' affiliate, the Oklahoma City Barons, recording 48 points to lead all AHL defencemen in scoring. He was ultimately awarded the AHL's Eddie Shore Award in 2012–13 as the league's top defenceman, despite participating in less than half of Oklahoma City's games.
Edmonton Oilers
Schultz later played his first NHL game in the first Oilers game following the 2012–13 NHL lock-out against the Vancouver Canucks. He scored his first goal during the next game, the Oilers' home opener, against Antti Niemi of the San Jose Sharks on January 22, 2013. On August 28, 2014, Schultz signed a new one-year contract with the Oilers valued at $3.675 million.
Pittsburgh Penguins
On February 27, 2016, with the Oilers out of playoff contention for the 2015–16 season, and suffering the worst season of his professional career with 10 points in 45 games, Schultz was traded to the Pittsburgh Penguins in exchange for a third-round pick in the 2016 NHL Entry Draft. On June 12, 2016, Schultz won the Stanley Cup with Pittsburgh after the team defeated the San Jose Sharks in the 2016 Stanley Cup Finals. On July 13, 2016, after testing free agency, Schultz returned to the Penguins, signing a one-year, $1.4 million contract. In the 2016–17 season, Schultz had a break-out year in his first full season with the Penguins, setting career-highs in goals, assists, points, penalties in minutes, power-play points and shots on goal. In addition, for the first time in his career, he finished a season with a positive plus-minus. His total number of assists, points, points per game played and plus-minus each finished within the top-ten in their respective categories among defencemen, and he emerged as the top blue-liner for the Penguins due to star defenceman Kris Letang being limited to only 41 games with various injuries. On June 11, 2017, Schultz won his second Stanley Cup title as a member of the Penguins after Pittsburgh defeated the Nashville Predators in the 2017 Stanley Cup Finals. On July 1, 2017, the first day of free agency, Schultz signed a three-year, $16.5 million contract to stay with Pittsburgh. In the 2017–18 season, Schultz suffered a lower-body injury in a game against the New York Rangers and was placed on injured reserve. He returned to the lineup on January 4, 2018, after missing 11 games. Schultz played in his 400th career NHL game on March 23, 2018, in a game against the New Jersey Devils. On October 13, 2018, just days into the 2018–19 season, Schultz broke his leg in Pittsburgh's game against the Montreal Canadiens. He was placed on IR and would not play until mid-February 2019. One week after his return, he then scored his first goal of the season in the 2019 NHL Stadium Series game against the Philadelphia Flyers.
