Born in Stuttgart, Winkelhock is the son of Formula One driver Manfred Winkelhock and nephew of Joachim Winkelhock, making him part of one of Germany's most prominent motorsport families. He began his single-seater career in junior formulae, winning races in Formula König, German Formula Renault, and the Formula Renault Eurocup between 1998 and 2000.
In 2001, Winkelhock entered the German Formula 3 Championship, spending three seasons in the series and recording a best championship finish of fourth in 2003. He tried touring car racing in 2004 with an AMG-Mercedes CLK in the DTM under the Persson team but failed to score points, then returned to single-seaters in 2005 in the World Series by Renault, where he won three times.
Winkelhock was confirmed as test and reserve driver for the Midland F1 team for the 2006 season, participating in Friday practice sessions at several rounds. The team was renamed Spyker F1 for 2007, and Winkelhock was retained in the same reserve role.
When Christijan Albers was released from Spyker after the 2007 British Grand Prix, Winkelhock was named as his replacement for the European Grand Prix at the Nürburgring — a one-race arrangement, with Sakon Yamamoto lined up for the remainder of the season.
Starting 22nd and last on the grid alongside teammate Adrian Sutil, Winkelhock's race was transformed by a last-second team decision on the formation lap. While every other driver started on dry-weather tyres on a damp but not yet wet circuit, Spyker called Winkelhock to the pits to switch to full wet tyres. When heavy rain arrived at the end of the first lap and forced the rest of the field to pit, Winkelhock was already circulating on the correct tyres and moved into the lead. He passed Kimi Räikkönen on track as the Ferrari driver tip-toed cautiously to the pit lane, and by the end of lap two held a 19-second advantage. By lap four his lead had extended to 33 seconds over Felipe Massa.
The stewards deployed the safety car and then suspended the race entirely after a series of incidents at Turn 1 behind the pace car. On the restart, Winkelhock and Spyker gambled on staying with full wet tyres on a rapidly drying track, hoping further showers would materialise. The gamble failed and he dropped rapidly through the order before retiring on lap 15 with hydraulic problems that caused a small fire. He had led for six laps in total.
Commentator Bob Varsha noted that Winkelhock became the only driver in Formula One history to start last on the grid and lead the race on his Grand Prix debut, and — owing to the red flag restart — the only driver to start both last and first in the same race. Despite the performance, Spyker did not offer him another race that season.
Winkelhock returned to the DTM after losing the Spyker seat, racing for Team Rosberg over three seasons from 2008 to 2010, finishing 12th, 10th, and 12th in the standings respectively.
In 2011, he joined the FIA GT1 World Championship with the All-Inkl.com Münnich Motorsport team alongside Marc Basseng, initially in a Lamborghini. After the team switched to the Mercedes SLS AMG for 2012 due to a regulation change, Winkelhock and Basseng won the championship.
He was due to move with Münnich Motorsport to the World Touring Car Championship for 2013, but departed before the season started to concentrate on GT racing, being replaced by defending WTCC champion Robert Huff.
From 2013 onwards, Winkelhock became a fixture in the Blancpain Endurance Series and its successor the GT World Challenge Europe. He also won the 24 Hours of Nürburgring in 2017, adding to his record at the Nordschleife. In mid-2021, he made a brief DTM comeback with Abt Sportsline, stepping in for Sophia Flörsch at the Nürburgring round while she fulfilled Le Mans commitments.
Winkelhock occupies a unique place in Formula One history for his rain-driven charge at the 2007 European Grand Prix — a six-lap stint at the front from last on the grid that remains one of the sport's more improbable stories. Beyond that single appearance, his career in endurance racing has been consistently high-level, marked by championship success in GT1 and GT Challenge competition and multiple victories at the Nürburgring 24 Hours.