[4] At the end of the 2013–14 Czech First League season, Ševčík started his career at Sigma Olomouc and made debuted as a second half substitute in a 5–0 away loss at Sparta Prague.
When Olomouc was subsequently relegated, he joined Opava on a half-season loan at the start of the 2014–15 Czech National Football League.
After the end of the season, he was one of two players who left Olomouc to transfer to Slovan Liberec alongside teammate Jan Navrátil, where Ševčík signed a three-year contract.
[8] On 18 April 2019, Ševčík scored a brace in the away second leg of the Europa League quarter-finals against Chelsea.
[10] In a UEFA Euro 2020 qualifying match against Kosovo on 14 November 2019, Ševčík debuted for the Czech senior squad, coming on as a substitute for Lukáš Masopust in the 76th minute.