Buhk began karting in 2004 in Germany, eventually reaching the KF2 category by 2009 when he placed fifth in ADAC Kart Masters. He made his single-seater debut in 2010 in the ADAC Formel Masters with KUG Motorsport, finishing twelfth. Staying in the series for 2011 but switching to ma-con after five rounds, he found his first podium results at Lausitz and Assen and climbed to ninth in the championship.
The 2012 season marked Buhk's decisive turn toward GT racing. Pairing with Dominik Baumann in the FIA GT3 European Championship aboard a Mercedes-Benz SLS AMG GT3, the two dominated the main category, winning half the races and taking the drivers' title. Alongside this campaign Buhk also competed in the ADAC GT Masters.
In 2013, following the merger of the FIA GT3 series into the new FIA GT Series, Buhk raced with Alon Day at HTP Motorsport. While results in that championship were limited, he expanded to the Blancpain Endurance Series where he delivered notable results — winning the 24 Hours of Spa and the season finale at the Nürburgring to claim the Endurance Series title. In the ADAC GT Masters, he partnered Maximilian Götz and won at the Nürburgring, finishing third overall.
Buhk contested multiple Blancpain GT championships through the mid-2010s with HTP Motorsport as his base operation. In 2014, three wins in the sprint series appeared to set him on course for a second championship title until a suspension for a safety car infringement during an ADAC GT Masters round forced him to miss the remainder of that series; his racing licence was eventually restored. The combined 2014 Blancpain GT Series standings saw him finish as runner-up to Laurens Vanthoor.
For 2015, HTP moved to the Bentley Continental GT3 for the sprint events, partnering Buhk with Vincent Abril. The combination produced three wins and the Blancpain GT Sprint Series title. In the endurance half of the series, contested with M-Sport alongside Andy Soucek and Maxime Soulet, the team collected points across the season outside of a retirement at the 24 Hours of Spa, finishing tenth overall.
The 2016 season brought Buhk's most complete Blancpain campaign. Reunited with Baumann in the new Mercedes-AMG GT3, the pairing overscored Rob Bell by ten points to take the overall Blancpain GT Series title — Buhk's most prestigious championship. They also finished second in the Endurance Cup and third in the Sprint Cup, adding a race win across the two sub-championships. A debut at the 24 Hours of Nürburgring that year ended in retirement.
In 2017 Buhk collected a third runner-up finish in the overall GT Series alongside new partner Franck Perera, with the pair taking a race win at Misano in the Sprint Cup. The Nürburgring 24 Hours again ended without a classified finish.
For 2018, HTP Motorsport shifted focus away from Blancpain towards the ADAC GT Masters, where Buhk partnered Indy Dontje. In the Blancpain Endurance Cup that year, Buhk joined Maximilian Götz and Álvaro Parente at Strakka Racing.
Buhk's final competitive years were spent in the Deutsche Tourenwagen Masters. After two seasons in the DTM, he announced his retirement from racing following the 2022 season, citing shifting personal priorities.
Across a decade of GT competition, Buhk won six major championship titles at the Blancpain and FIA GT level and triumphed at the 24 Hours of Spa in 2013. His partnership with HTP Motorsport and Mercedes-AMG produced consistent results at the top level of European GT racing, placing him among the most decorated German GT drivers of his generation.