Carolina Hurricanes

At the conclusion of the 2014–15 season with the Whalers, Nedeljkovic signed a three-year, entry-level contract with the Carolina Hurricanes on March 27, 2015. He was assigned to the ECHL affiliate, the Florida Everblades, to make his professional debut in the final regular season games.^[7]

During his final season of junior in the 2015–16 season, Nedeljkovic was traded by the Flint Firebirds, along with fellow Hurricanes draft pick Josh Wesley, to the Niagara IceDogs in exchange for goaltender Brent Moran in November 2015.^[8]

In his rookie professional season in 2016–17, on December 30, 2016, while playing for the Florida Everblades, Nedeljkovic became the 12th ECHL goaltender to score a goal.^[9] On January 17, 2017, Nedeljkovic played his first NHL game, in relief of starter Cam Ward against the Columbus Blue Jackets.^[10]

During the 2017–18 season, on March 10, 2018, while playing for the Charlotte Checkers in a game against the Hartford Wolf Pack, Nedeljkovic became the 13th goaltender in the American Hockey League (AHL) history to score a goal.^[11]

After starting the 2018–19 season with the Checkers, Nedeljkovic was recalled to the NHL on January 17, 2019.^[12] On January 23, against the Vancouver Canucks, he made his first NHL start in which he made 24 saves on 26 shots to secure his first win in the NHL.^[13]

On June 28, 2019, Nedeljkovic signed a two-year contract extension with the Hurricanes.^[14]

In the pandemic-delayed 2020–21 season, Nedeljkovic remained with the Hurricanes due to the expanded roster, and responded with a break-out season in the NHL. On February 20, 2021, in a 4–0 victory over the Tampa Bay Lightning, Nedeljkovic recorded his first career NHL shutout.^[15] On April 1, Nedeljkovic was named NHL's Rookie of the Month for games played in March.^[16] In 23 regular season games, he posted a 15–5–3 record for the division-leading Carolina and tied for the NHL rookie lead in shutouts alongside Ilya Sorokin with three. Nedeljkovic recorded a 1.90 goals-against average and .932 save percentage to led all NHL goaltenders who played at least 20 games. On May 17, Nedeljkovic got his first Stanley Cup playoffs win with a 5–2 win over the Nashville Predators.^[17] On May 19, Nedeljkovic recorded his first Stanley Cup playoffs shutout with a 3–0 victory over the Predators.^[18] He collected four wins in nine postseason games, unable to help propel the Hurricanes past the second-round. In June 2021, Nedeljkovic was a finalist for the Calder Memorial Trophy, given to the NHL's rookie of the year, placing third behind Kirill Kaprizov and Jason Robertson, and was named to the NHL All-Rookie Team.^[19]

Detroit Red Wings

As a restricted free agent, unable to agree to terms on a new contract with the Hurricanes, Nedeljkovic was traded to the Detroit Red Wings in exchange for Jonathan Bernier and a third-round pick in 2021 on July 22, 2021. He was immediately signed to a two-year, $6 million contract by the Red Wings.^[20]

Nedeljkovic would record his first shutout as a member of the Red Wings on January 15, 2022, over the Buffalo Sabres with several family members in attendance at Little Caesars Arena. After a strong fall start to his first season with the Red Wings, Nedeljkovic struggled in the New Year, having gone 2–5–1, with a 4.64 goals against average and .849 save percentage in his previous nine appearances by the beginning of March.^[21] He made headlines on March 10, when he accidentally scored an own goal by sweeping into the net a puck that had been traveling wide of it, dubbed a "gaffe for the ages" by the Detroit Free Press.^[22]

Pittsburgh Penguins

On July 1, 2023, Nedeljkovic signed a one-year, $1.5 million contract with the Pittsburgh Penguins.^[23] On November 17, during a rehab stint with the Wilkes-Barre/Scranton Penguins, Nedeljkovic scored his second goal at the AHL level in a 4–2 road win over the Providence Bruins. He became the first goaltender in AHL history to score two or more career goals.^[24]