After two solid seasons with the USA Hockey National Team Development Program, Fischer, a Chicago native, was selected by the Arizona Coyotes in the second round (No. 32) of the 2015 NHL Draft. He signed with Arizona on Aug. 20, 2015, and joined Windsor of the Ontario Hockey League, finishing with 90 points (40 goals, 50 assists) in 66 games before turning pro.

Fischer, a 6-foot-2 forward, played most of the 2016-17 season with the Coyotes' American Hockey League affiliate in Tucson, putting up 47 points (team-high 20 goals, 27 assists) in 57 games. He made his NHL debut Jan. 21, 2017 and scored a goal on his first shot in Arizona's 5-3 victory against the Tampa Bay Lightning.

He scored again two nights later against the Florida Panthers on his only shot on goal but played one more game before being returned to Tucson. When he was recalled in late March, he scored again against the Lightning, also on his first shot, on March 26, giving him three goals on his first three NHL shots.

Fischer won a spot on the Coyotes after training camp in 2017-18 as a 20-year-old and showed good speed, a quick wrist shot and a big slap shot, and had his first career NHL hat trick in a 4ñ1 win against the Columbus Blue Jackets on Oct. 23.

Fischer scored the first two NHL goals at Mullett Arena, the temporary home of the Coyotes on the campus of Arizona State University, in a 3-2 overtime loss to the Winnipeg Jets on Oct. 28, 2022. After playing his first seven NHL seasons for Arizona, Fischer signed a one-year, $1.125 million contract with the Detroit Red Wings on July 2, 2023, and then a one-year, $1.125 million contract July 1, 2024.

Fischer retired from the NHL on July 4, 2025, after nine seasons.