Vetter was born and raised in Dresden. Upon receiving his Abitur, he joined the ' and has been a ' since September 2014. He has a tattoo of an Ancient Greek javelin thrower on his back.
Career
In 2011, Vetter competed in the European Junior Championships. He made it through the qualifying round with a personal best 71.60 m throw. He then finished 12th in the final with a throw of 65.87 m. Zigismunds Sirmais won the event with a throw of 81.53 m. In July 2015, Vetter took part in the European U23 Championships. He finished fourth, throwing the javelin 79.78 m. Kacper Oleszczukwon gold with a throw of 82.29 m. In August 2015, he competed in the IAAF World Championships. He finished seventh with a throw of 83.79 m. Julius Yego won the competition with a throw of 92.72 m. Vetter competed for Germany at the 2016 Summer Olympics, along with Julian Weber and eventual gold medalist Thomas Röhler. Leading up to his maiden Olympics, Vetter unleashed the javelin with a personal best of 88.23 m to top the field and attain the Olympic entry standard by a five-centimetre margin at the Kuortane Games in Finland. Coming to the final with the second best throw at 85.96 m from the qualifying stage, Vetter opened the competition with an 85.32 m throw on his first attempt to seize an early lead, but Röhler, along with 2015 World Champion Julius Yego of Kenya and defending Olympic Champion Keshorn Walcott of Trinidad and Tobago overtook him for the medal positions. Unable to improve his mark in the remaining attempts, Vetter finished in fourth place, outside the podium by just six centimetres. Less than a month after his disappointment at the Olympics, Vetter finished first in a world-class field at the 2016 ISTAF Berlin, throwing a personal best of 89.57 m. In July 2017, he won the German Championship with a throw of 89.35 m. This was his first victory in the German Championship. Two days later, he recorded throws of 90.75 m, 91.06 m, 93.06 m and a personal best 94.44 m at the 2017 Spitzen Leichtathletik Luzern. The 94.44 m throw was also a German record, besting Röhler's 93.90 m throw from May 2017. In August 2017, he won gold at the World Championships in London with a throw of 89.89 m. Vetter finished his season at the 2017 ISTAF Berlin, where he won gold with an 89.85 m throw, nearly four metres ahead of second place Röhler. On 14 October 2017, he won the 2017 European Athlete of the Year Trophy. In March 2018, he won gold at the European Throwing Cup, throwing 92.70 m, twelve metres ahead of second place. In July, he won bronze at the 2018 German Athletics Championships, with a throw of 87.83 m. In August, he competed in the 2018 European Athletics Championships. He won the qualifying round with an 87.39 m effort, then placed fifth in the final with a throw of 83.27 m. Röhler won gold with 89.47 m. Vetter represented Team Europe at The Match Europe v USAin September 2019. He won gold with a throw of 90.03 m, his best performance since May 2018. At the 2019 World Athletics Championships, Vetter had the best throw in the qualifying round, with 89.35 m. He then won bronze in the final, throwing 85.37 m.