Vít Müller gained his first international experience in 2015 when he was eliminated in the first round at the Junior European Championships in Eskilstuna with 54.84 seconds. The following year he qualified for the first time for the European Championships in Amsterdam , where he was eliminated in the semifinals with 50.70 s. At the IAAF World Relays 2017 in the Bahamas , he finished fourth in the B-final with the Czech 4-by-400-meter relay in 3: 08.17 min and then reached 50 at the U23 European Championships in Bydgoszcz , 63 s eighth place. Then he reached the semifinals at the Summer Universiade in Taipei , where he was eliminated with 51.46 minutes. In addition, he won the bronze medal behind the teams from the Dominican Republic and the United States in 3: 08.14 min. In 2018 he retired at the World Indoor Championships in Birmingham with the relay in 3: 06.40 min in the preliminary round. He also qualified again for the European Championships in Berlin , where he was eliminated in the first round with 51.00 s. He was also used in the relay and helped the Czech team to reach the finals. In 2019 he was eliminated from the European Indoor Championships in Glasgow with 47.69 seconds in the 400-meter run . He then finished third in the B final at the World Relays in Yokohama in 3: 03.79 minutes. At the Student World Games in Naples he was eighth in the individual competition in 50.86 s and finished fifth with the relay in 3: 06.78 min. He also qualified for the first time for the World Championships in Doha and reached the semi-finals there , in which he was eliminated with 49.97 s. Before that, he won the silver medal behind the team from Ukraine in the mixed relay at the European Games in Minsk in 3: 17.53 minutes.
In 2017, 2019 and 2020 Müller became Czech champion in the 400-meter hurdles and in the 4-by-400-meter relay outdoors. In the hall, he became champion in the 4 x 200 meter relay in 2019.