Müller, the sports soldier from Bludenz , made his first international appearance at the 2015 European Junior Championships in Oberhof . There he finished sixth. In the 2015/16 season he won three Junior World Cup victories, two of them in the single-seater and one in the relay. He also achieved third place and second place once, winning the Junior World Cup. At the Junior European Championships 2016 in Altenberg he won the gold medal in the single seater and was fifth at the Junior World Championships in Winterberg in early February 2016 . At the beginning of the 2016/17 season, he started the Luge World Cup in Lake Placid for the first time and came in 22nd. Three more participations in the World Cup followed. His best placing was 17th in Sigulda and thus reached 37th place in the overall World Cup. At the highlight of the season, the 2017 Luge World Championships in Innsbruck-Igls , he finished 21st in the single-seater. In the 2018/19 season he made it into the top ten four times in the World Cup. The fourth place in the single seater at Königssee was his best placement and thus reached eleventh place in the overall World Cup.
At the end of January 2019, he surprisingly won the gold medal in the sprint race at the Luge World Championships in Winterberg.
Jonas Müller, men's sprint world champion, January 2019
At the beginning of the 2019/20 season, Müller won his first World Cup victory in a single-seater in Innsbruck-Igls. He also won second place there with the relay. He also won the following single-seater race at the World Cup in Lake Placid, where he also finished third in the sprint race. He repeated this placement in mid-December 2019 at the third World Cup station in Whistler .