Montoya began kart racing at age five, trained by his father Pablo, who remortgaged the family home to fund his son's career without his wife's knowledge. He won multiple Colombian karting titles from 1984 to 1989 and attended a Skip Barber Racing School at Sonoma Raceway in 1992. He won the Nacional Tournament Swift GTI Championship in 1993 with seven victories from eight races.
After winning the 6 Hours of Bogotá in 1995 and competing in the Formula Vauxhall Lotus Championship under Paul Stewart Racing's guidance, Montoya moved to the British Formula 3 Championship in 1996, finishing fifth. He won the International Formula 3000 Championship in 1998 with Super Nova Racing after a seven-race winning season that followed his runner-up finish in 1997 with RSM Marko.
Montoya signed with Chip Ganassi Racing for the 1999 CART season after Frank Williams chose Alex Zanardi over him for a Williams Formula One seat. He won seven races and became CART's youngest champion and the second rookie champion in series history, edging Dario Franchitti on equal points by virtue of race wins. That same year, racing in the rival Indy Racing League's Indianapolis 500, Montoya led 167 of 200 laps from second on the grid to win, becoming the first rookie winner since Graham Hill in 1966.
Montoya debuted in Formula One with Williams in 2001, replacing Jenson Button. He won his maiden race at the Italian Grand Prix from pole position, leading 29 laps, and became the first Colombian winner in Formula One history. He finished sixth in the championship.
In 2002, Montoya qualified on pole position seven times but mechanical fragility limited him to third in the Drivers' Championship with 50 points. His 2003 season was his strongest, winning the Monaco Grand Prix and the German Grand Prix by over a minute from pole, ultimately finishing third in the championship with 82 points, eleven short of the title. He closed out his Williams tenure by winning the 2004 Brazilian Grand Prix and ended fifth in that year's championship.
Montoya joined McLaren for 2005 alongside Kimi Räikkönen. Missing two races due to a shoulder fracture, he won the British, Italian, and Brazilian Grands Prix and finished fourth in the championship. His McLaren tenure ended mid-2006 after friction with team management; he was replaced by Pedro de la Rosa following the United States Grand Prix and left Formula One having scored seven race victories.
Montoya switched to the NASCAR Cup Series with Chip Ganassi Racing in 2007. He won the Toyota/Save Mart 350 at Infineon Raceway, becoming the first foreign-born Cup Series winner since Earl Ross in 1974. He also won the Telcel-Motorola Mexico 200 in the Nationwide Series. His best Cup Series season was 2009, when he qualified for the Chase for the Sprint Cup and finished eighth in the points standings. A second Cup victory came in 2010 at Watkins Glen. He left full-time NASCAR competition after 2013.
Montoya returned to IndyCar with Team Penske in 2014 and won the Pocono IndyCar 500 in the fastest 500-mile race in series history at that time. In 2015, he won the Indianapolis 500 for a second time, passing Will Power with three laps to go, and ended second in the championship on a tiebreaker with Scott Dixon. A final IndyCar victory came at the 2016 Firestone Grand Prix of St. Petersburg.
Montoya won the 24 Hours of Daytona three times: in 2007 and 2008 with Chip Ganassi Racing and in 2013. He joined Team Penske's IMSA programme full-time in 2018, and in 2019 won the IMSA Prototype drivers' championship alongside Dane Cameron with three race victories. He also competed at the 24 Hours of Le Mans in 2017 with United Autosports, finishing third in LMP2.
Montoya's career is notable for its breadth, aggression, and the genuine belief that he could have won a Formula One world championship with different circumstances. His ability to win at every level he contested — CART, IndyCar, Formula One, NASCAR, and IMSA — places him among a handful of drivers whose competitiveness was not tied to any single car or discipline. His direct, combative driving style drew both admiration for its spectacular quality and criticism for its frequency of incident. The 2001 Italian Grand Prix victory, achieved on debut at Monza from pole position, remains one of the most emphatic maiden Formula One wins of the modern era.