Kyburz won the Sprint World Junior Championship in Italy in 2009. In 2011 he caused a stir when he won the World Cup opener in Porvoo . In the course of the World Cup season, he also came third twice. In the overall standings, he finished fourth behind Daniel Hubmann , Thierry Gueorgiou and Matthias Merz . At the 2011 World Championships in France, Kyburz also won his sprint qualification, but only came 20th in the final.
At the European Championships in 2012 Kyburz came in sixth in the sprint and sprinted to gold for Team Switzerland 2 in the relay on the final stretch. At the orienteering world championships in Lausanne in 2012 Matthias Kyburz won the gold medal in the sprint ahead of his two teammates Matthias Merz and Matthias Müller . At the World Games 2013 in Colombia, Kyburz became the most successful orienteer of these games. In the sprint he won just before the Russian Andrey Khramov and the Swede Jerker Lysell . In the middle distance he prevailed against his Swiss teammate Daniel Hubmann and the Lithuanian Vilius Aleliūnas . In the end, Kyburz won his third gold medal, which he clearly won with the mixed relay (together with Daniel Hubmann, Sara Lüscher and Judith Wyder ) in front of the teams from Denmark and Austria.
On April 16, 2020, Kyburz improved the world record over the 50-kilometer distance on a treadmill with his time of 2:56:35 h.
