Brabec was part of the youth system at Sparta Prague, but having been released in summer 2008, he joined Viktoria Žižkov, another Prague-based club.

[2] He made one league appearance for the club in this season, playing a full match against Viktoria Plzen as a 16-year-old in a 2–0 defeat.

He scored his first national goal on his third and final appearance for the Czech Republic under-18s in a 3–1 loss to the Austria under-18s in a March 2010 friendly match.

He scored a header in a group game tournament fixture against the Republic of Ireland under-19s to equalise 1–1 on 23 July 2011; the Czechs went on to win 2–1.

[15] On 11 October 2019, Brabec scored his first goal in a UEFA Euro 2020 qualifying match against England, resulting in a 2-1 victory for the Czechs.

[16] On 19 November 2023, along with Vladimír Coufal and Jan Kuchta, Brabec has been kicked out of the Czech Republic's national team camp after they allegedly going out clubbing two days before the Euro 2024 qualifier match against Moldova.