Matěj Kovář was born on 17 May 2000 in Uherské Hradiště, Czech Republic, and began his footballing development at 1. FC Slovácko before making the move to Manchester United's academy in January 2018 at just 17 years old. He spent several seasons developing within United's youth setup, gaining senior experience through a series of loan spells at Swindon Town, Burton Albion, and Sparta Prague.
His time at Sparta Prague proved to be a turning point. Kovář established himself as first-choice goalkeeper, making 28 league appearances and earning the Czech First League Goalkeeper of the Season award while helping the club to its first league title since 2013–14. That form attracted the attention of Bayer Leverkusen, who signed him on a four-year deal in August 2023 for a fee of up to £7.7 million. At Leverkusen he added three more honours to his CV — the Bundesliga, DFB-Pokal, and DFL-Supercup — before joining PSV on a permanent contract in January 2026.
A composed, technically capable shot-stopper, Kovář is now a key fixture between the posts for PSV, with whom he won the Eredivisie in 2025–26.
At international level, Kovář has represented the Czech Republic from under-18 through to the senior side. He made his senior debut in a friendly against Armenia in March 2024 and was part of the Czech squad at UEFA Euro 2024, making an appearance in the group-stage defeat to Turkey.