Metalurh Zaporizhzhia Born in
Zaporizhzhia, Ukraine, Kryvtsov is a product of the
Metalurh Zaporizhzhia Youth school system, where he was trained by Viktor Tryhubov. He made his debut for the club at the age of 17 in a 1–1 draw with
Chornomorets Odesa on 3 May 2008. His first goal for the club came in a 2–0 victory over
Illichivets Mariupol on 27 February 2010. He left the club in May 2010 to join
Shakhtar Donetsk for an undisclosed fee.
Shakhtar Donetsk On 11 May 2010, Kryvtsov, along with
Taras Stepanenko, signed for
FC Shakhtar Donetsk from
Metalurh on a five-year deal. His first appearance for the club came on 10 November 2010 in a 1–0
Ukrainian Cup victory over his old club, Metalurh Zaporizhzhia. He made a further two appearances in his first season, both coming in the league. Shakhtar won the treble with success in the
Premier League,
Cup and the
Super Cup. The following season he made six appearances for the club, five of which came in the league, as Shakhtar clinched the
Premier League title and the
Ukrainian Cup. He made his first appearance of the
2012–13 season on 26 August in a 3–0 victory over
Karpaty Lviv at the
Donbas Arena. He played the full 90 minutes, picking up a yellow card in the 85th minute. He also played in a 3–1 victory over
Dynamo Kyiv as a 70th-minute substitute, replacing the injured
Oleksandr Kucher who scored twice.
Inter Miami In January 2023, Kryvtsov joined
Major League Soccer club
Inter Miami on a two-year deal, with an option for a third-year extension. In his debut game for the club, Kryvtsov netted the opening goal of the match as Inter Miami defeated
CF Montréal 2–0. As a result, he was named to the league's Team of the Matchday for week one.In December 2024, Inter Miami chose to not renew his contract so he left the club, before retiring from the sport in March 2026. ==International career==