[3] He made his international debut at the 2006 Junior European Championships where he helped the Romanian team place fifth.

[12] Muntean won bronze medals on both the still rings and parallel bars at the 2015 Doha World Challenge Cup, and he placed fourth on the vault.

[3] At the Olympics, Muntean finished 36th in the all-around during the qualification round, and he qualified for the parallel bars final.

[23] Individually, he qualified for the vault final where he won the bronze medal behind Audrys Nin Reyes and Oleg Verniaiev.

[26] Muntean won the silver medal on parallel bars at the 2018 Koper World Challenge Cup behind Đinh Phương Thành.

[27] Then at the Guimarães World Challenge Cup, he won silver medals on the rings and on the parallel bars, both behind Manrique Larduet.

[29] He won the overall World Challenge Cup parallel bars titles for having the best results across the series, and he was second on the still rings behind Çolak.

[3] There, he won the silver medal on the parallel bars behind Ukraine's Petro Pakhnyuk, and he placed fifth on rings.

[37] Then at the Mersin World Challenge Cup, he won a bronze medal on parallel bars and placed fourth on rings and sixth on floor exercise.

[40] Then at the 2023 World Championships in Antwerp, Muntean finished 30th in the all-around during the qualification round, making him the fourth reserve for the final.

As the eighth highest-ranked gymnast from a country that did not qualify a full team, he received an individual quota for the 2024 Olympic Games.

[41] Muntean began the Olympic season at the Antalya World Challenge Cup where he won the bronze medal on the parallel bars behind Nicolau Mir and Radomyr Stelmakh.