He made his debut for Viktoria Plzeň against Baník Sokolov on 12 November 2011 in the Czech Cup. After multiple seasons and becoming a starting XI regular, as well as praise for his performances in 2018–19 UEFA Champions League, it was rumoured that Hrošovský will join one of La Liga's or Premier League's teams - Levante, Getafe and Huddersfield were all named as possible future clubs. During the winter transfer window however, Hrošovský failed to make a transfer. Later during January 2019 transfer window, West Ham was also cited as a contender for his services, however it was dropped as Manuel Pellegrini doesn't favour altering the squad during the season.
Genk
2019–20 season
On 5 June 2019, as Hrošovský was preparing with the national team for a double fixture against Jordan and Azerbaijan, it was reported that he was very close to a transfer to Genk. Verbal agreement was apparently complete, yet an issue arose, as Viktoria was happy to let Hrošovský go later during the summer transfer period, in order to help them qualify to the group stage of the Champions League. Genk was said to oppose this arrangement. Nonetheless, it was said that the transfer was more-or-less a done deal, as Plzeň agreed with Wolverhampton Wanderers on a two year loan, with an option to buy for Christián Herc, who had made a good impression during his loan at DAC Dunajská Streda, and was seen as a replacement for Hrošovský. On the following day, Hrošovský however calmed the rumours, during a press conference prior to the match against Jordan, stating that while negotiations did take place, there is no certainty of a transfer and that he is still a player of Plzeň. Regardless, this arrangement was confirmed on 8 July 2019, as Hrošovský signed a 4-year contract, with an option for an additional year. He made his Jupiler Pro League debut against multiple-time champions Anderlecht Brussels, in a home fixture on 23 August 2020. He completed the last, roughly, 20 minutes, as a replacement for Jakub Piotrowski. Genk secured a narrow 1:0 win with a second-half goal by Mbwana Samatta. Hrošovský had recorded five starts for Genk in the UEFA Champions League. He played in both matches against Napoli and Red Bull Salzburg. He played against Liverpool at Anfield only. Genk, however, collected a sole point, for a goal-less tie against Napoli and was knocked out with a score of 5:20. On top of that, Hrošovský made sole seasonal appearance in the Croky Cup in a Round of 16 loss against Royal Antwerp. Genk were knocked out after a penalty shoot-out. Hrošovský was replaced by Théo Bongonda in the second half. As an occasional scorer, Hrošovský had to wait until 1 February 2020 for his first goal at Genk. In a league fixture against Charleroi, he had beaten Nicolas Penneteau with a back-heel goal in the 39th minute, utilising a pass from Junya Ito. He was replaced by Kristian Thorstvedt in the second-half. Genk won 1:0.
