Schmidt has become an NHL regular despite being undrafted following his senior season at St. Cloud Cathedral High School in Minnesota in 2008-09. He had finished as the second-highest scoring defenseman in the state (21 goals, 45 points) and led his team to the Class A state semifinals.

The native of St. Cloud, Minnesota, had 37 points (14 goals, 23 assists) with Fargo of the United States Hockey League in 2009-10 before heading to the University of Minnesota. He didn't play much as a freshman, but blossomed in his sophomore season, leading all college defensemen with 38 assists. He had 32 points (nine goals, 23 assists) as a junior.

That was enough to attract the interest of the Washington Capitals, who signed him as a free agent on April 2, 2013. He finished the season with Hershey of the American Hockey League, scoring one goal and finishing with four points in eight regular-season games as well as two assists in five Calder Cup playoff games.

Schmidt split his first two pro seasons between Washington and Hershey, appearing in 68 NHL games. Schmidt made his NHL debut on Oct. 12, 2013, against the Colorado Avalanche and scored his first goal against the Nashville Predators on Dec. 7, 2013.

He stuck with the Capitals for good in 2015-16, but played mostly on the third pair. That changed when he was selected by the Vegas Golden Knights in the 2017 NHL Expansion Draft. His average time on ice jumped to 22:14 from 15:29, and he had NHL career highs in assists (31) and points (36). Schmidt also played all 20 games for the Golden Knights during the Stanley Cup Playoffs, which ended with a five-game loss to his former team in the Cup Final, finishing with seven points (three goals, four assists).

Schmidt scored nine goals and led the Golden Knights in average ice time (21:57) in 2018-19. He finished with 31 points (seven goals, 24 assists) and averaged 21:41 in 2019-20.

Schmidt was traded to the Vancouver Canucks for a third-round pick in 2022 NHL Draft on Oct. 13, 2020, but after scoring 15 points (five goals, 10 assists) in 54 games for a Canucks team that struggled, finishing last in the Scotia North Division, he was traded for a third-round pick in the 2022 draft, this time to the Winnipeg Jets on July 27, 2021.

Schmidt signed a one-year contract with the Florida Panthers on July 3, 2024, becoming an unrestricted free agent July 1 after the Winnipeg Jets bought out the final season of his contract. He became a Stanley Cup champion for the first time when the Panthers defeated the Edmonton Oilers 5-1 in Game 6 of the 2025 Stanley Cup Final. Schmidt was the first to be handed the Cup by Florida captain Aleksander Barkov and was the first of many Panthers who held the it for the first time. He gave it to Seth Jones, another longtime NHL defenseman. It then went to Tomas Nosek, Vitek Vanecek, A.J. Greer, Jesper Boqvist, Mackie Samoskevich, Uvis Balinskis, Jaycob Megna and third-string goalie Evan Cormier.

Schmidt signed a three-year contract with the Utah Mammoth on July 1, 2025.