Zelený made his debut in the league in 2011 in Hradec Králové. Three years later, he moved to Karviná, with whom he won second division. Subsequently, he movedd to Jablonec. In the summer 2018, he moved to Slavia, where he won two titles and played in the Champions League and Europa League. However, he did not have a permanent place in the line-up and returned to Jablonec in 2020. Thanks to his good performances, he got to the Czech national team. In the summer 2022 he moved to Sparta.