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Malinovskyi began his career at local side Polissya Zhytomyr under the management of Serhiy Zavalko.
Malinovskyi was a member of the Ukraine national under-19 team. From 1 September 2012, he played on loan for Sevastopol, signing a one-and-a-half-year contract.
From 2011, Malinovskyi was a player of Shakhtar Donetsk, who sent him on loan to different clubs. He played for Shakhtar-3 from 2010 to 2012, playing 39 matches and scoring 10 goals. He made no appearances for Shakhtar's first team.
In 2014, Malinovskyi went on loan to Zorya Luhansk, where he became a main player in the team. He was recognised as the best young player in Ukraine. Malinovskyi scored goals not only in the Ukrainian Premier League, but also twice in the UEFA Europa League against Belgian side Charleroi.
On 1 January 2016, it was officially announced that Malinovskyi would be loaned to Belgian side Genk until the end of the season. He debuted for the club in the Belgian Cup semi-final against Standard Liège and spent 72 minutes on the field.
On 16 July 2019, Malinovskyi signed for Atalanta for €13.7 million. On 22 October 2019, he scored his first goal for Atalanta in the UEFA Champions League game against Manchester City. Malinovskyi was named Player of the Month by Atalanta supporters. He scored his first Serie A goal on 7 December 2019 in a match against Hellas Verona. On 24 June 2020, Malinovskyi scored the equalizing goal in a 3–2 comeback win against Lazio. On 18 April 2021, he scored the winning goal in a 1–0 win over Juventus; this was Atalanta's first win against Juventus in Serie A since February 2001. On 19 May 2021, he scored in the final of the Coppa Italia against the same opponents but Atalanta fell to a 1–2 defeat.