[2] In September 2010 he went on a trial at Real Zaragoza, but could not sign with the club due to his age;[3] he later returned to Russia and joined FC Spartak Moscow's youth setup.

He made his senior debuts with Zaragoza's reserves in the 2011–12 campaign, appearing rarely in Segunda División B.

On 23 March 2014 Shvets played his first match as a professional, coming on as a late substitute in a 0–1 home loss against Deportivo de La Coruña in the Segunda División championship.

[2] He played his first full international for his country on 27 March 2018 against France, replacing Alexandr Yerokhin, the game Russia lost with a score of 1–3.

[10] On 11 May 2018, he was included in Russia's extended 2018 FIFA World Cup squad as a back-up,[11] but was excluded from the final list.