In 2012, soon after his move to Kazan in 2010, Svechnikov began his junior career playing for Bars and Irbis, junior teams of the Ak Bars Kazan club system. He made his pro debut with Ak Bars before reaching the age of 17, during the 2013–14 season. Svechnikov was drafted in the second round, 63rd overall, in the 2013 CHL Import Draft by the Cape Breton Screaming Eagles and committed to the organization for the 2014–15 season. In his rookie season, he finished third in club scoring, and ranked second among QMJHL rookies with 32 goals and 46 assists in 55 games. He led his team in points-per-game at 1.42. Following an outstanding rookie season, he was named to the QMJHL All-Rookie Team and featured in the CHL/NHL Top Prospects Game. On 26 June 2015, Svechinkov was drafted 19th overall by the Detroit Red Wings in the 2015 NHL Entry Draft. On 2 October 2015 the Red Wings signed Svechinkov to a three-year, entry-level contract. During the 2015–16 season, Svechnikov recorded 32 goals and 47 assists in 50 games. His 79 points ranked second on the team and tied for 18th in the QMJHL, while his 47 assists placed 17th and his 13 power play goals tied for eighth. On 24 April 2016, Svechnikov was assigned to the Grand Rapids Griffins of the American Hockey League. On 3 April 2017, Svechnikov was recalled by the Red Wings. Prior to being recalled he recorded 18 goals and 26 assists in 68 games for the Griffins. He led all Griffins rookies in points and ranked among the top AHL rookies in goals, points, game-winning goals and shots. He made his NHL debut for the Red Wings later that night in a game against the Ottawa Senators. In his debut, he scored the game-winning goal in a seven-round shootout. He was assigned to the Griffins on 5 April. He played two games with the Red Wings, recording four shots in 13:08 average time on ice. During the 2016–17 season, he ranked third on the Griffins with 20 goals and 31 assists in 74 regular-season games and added five goals and seven assists in 19 playoff games, to help lead the Griffins to the Calder Cup. On 8 March 2018, Svechnikov was recalled by the Red Wings. After producing just five points over the Griffins's first 26 games this season, Svechnikov has recorded five goals and 12 assists in 25 games since 30 December 2017, including eight points in his last 11 games. On 20 March, Svechnikov scored his first career NHL goal against Petr Mrázek of the Philadelphia Flyers. On 4 April, Svechnikov was assigned to the Griffins. He appeared in 14 games for the Red Wings, posting two goals, two assists, eight penalty minutes, 15 shots on goal, 15 hits and six blocked shots. On 16 October 2018, Svechnikov underwent anterior cruciate ligament reconstruction surgery on his right knee due to an injury he sustained in the Red Wings final preseason game against the Toronto Maple Leafs on 29 September 2018. He missed the entire 2018–19 season.
