Born in Mykolaiv, Shved is a product of the FC Karpaty Lviv youth system, where he joined at the age of seven.

Shved made his debut for Karpaty in a game against FC Metalurh Donetsk on 1 March 2015 in the Ukrainian Premier League, playing the full 90 minutes of a 1–1 draw in Kyiv's Obolon Arena.

[2] He turned down fellow Spaniards Valencia CF to sign for the Andalusians, also being attracted by the presence of compatriot Yevhen Konoplyanka in the team.

[4] On 4 October 2015, Shved made his senior debut for Sevilla Atlético, replacing José Amo for the final eleven minutes of a 1–1 draw at UD Marbella.

[9] In January 2019, he signed an 18-month contract with Scottish Premiership club Celtic but remained at Karpaty on loan for the remainder of the season.