The Washington Capitals played the long game with Fehervary, a defenseman they selected in the second round (No. 46) of the 2018 NHL Draft. He played his first full season for HV71 of the Swedish Hockey League after signing a three-year, entry-level contract with the Capitals on July 1, 2018, a plan designed to get him ready for a move to North America and a development path similar to those of centers Nicklas Backstrom (No. 4, 2006 NHL Draft), Marcus Johansson (No. 24, 2009 NHL Draft) and Evgeny Kuznetsov (No. 26, 2010 NHL Draft) took on their way to the Capitals.

Fehervary attended his first NHL training camp before the 2019-20 season, after having moved to Sweden from his native Slovakia to live with a billet family when he was 14 and on his own since age 15. He played four games in the SHL as a 16-year-old with Malmo in 2015-16 and nine more in 2016-17, and 42 games for Oskarshamn in Sweden's second-highest league in 2017-18.

"It was a great experience, a life experience," Fehervary told NHL.com. "I think it helped me a lot in my social life too, and with hockey the most."

Fehervary made his NHL debut Oct. 2, 2019 and scored his first NHL point, an assist, Feb. 8, 2020, four days before the NHL paused the season due to concerns surrounding the coronavirus. He scored his first NHL goal in a 4-3 overtime loss to the Calgary Flames on Oct. 23, 2021.

Fehervary signed a three-year, $8.025 million contract with the Capitals on July 4, 2023, an average annual value of $2.675 million. He was a restricted free agent who had 16 points (six goals, 10 assists) in 2022-23. Fehervary averaged 20:00 per game, including 18:19 at even strength that ranked third among Washington defensemen. He also led Capitals defensemen with 217 hits and his 128 blocked shots were second to Trevor van Riemsdyk (160).

Fehervary signed a seven-year, $42 million contract with the Capitals on July 1, 2025. He set NHL career highs in assists, points and games played in 2024-25, and had the fastest maximum skating speed (23.34 mph) among Capitals skaters and ranked in the 95th percentile among NHL defensemen in top skating speed, per NHL EDGE. His four assists in six games for Team Slovakia at the Olympic Winter Games Milano Cortina 2026 tied Lubomir Sekeras (four at the 1998 Nagano Games) for the most by a Slovakian defenseman in an Olympics involving NHL players.