Rosenqvist began his single-seater career in Asia, winning the Formula Renault 2.0 Asia championship in 2008 and the Formula Renault 2.0 Sweden/NEZ title in 2009. He moved to the German Formula Three Championship in 2010, finishing fifth with two victories, eight podiums, and one pole position while also qualifying seventh in his debut at the Macau Grand Prix.
In 2011, he stepped up to the Formula 3 Euro Series with Mücke Motorsport, finishing fifth as a rookie with one win and ten podiums, and winning the prestigious Masters of Formula 3 in his debut appearance. He finished third in the 2012 championship and second at the Macau Grand Prix. In 2013, he narrowly missed the European F3 title to Raffaele Marciello but won the Masters of Formula 3 for a second consecutive year. After a quieter 2014 season in which he won the Macau Grand Prix from pole position ahead of teammate Lucas Auer, he joined Prema Powerteam for 2015 and dominated, winning 13 races with 24 podiums and 17 pole positions to claim the European Formula 3 Championship title. By the end of his extended Formula 3 career, Rosenqvist had become the most successful Formula 3 racer of all time by victories.
Rosenqvist entered the Deutsche Tourenwagen Masters in 2016 as the official reserve driver for Mercedes-Benz, but was promoted to a race seat with ART Grand Prix mid-season following Esteban Ocon's departure to Manor Racing in Formula One. He made an impressive DTM debut in Moscow, scoring points with a tenth-place finish in his first-ever start in the series. His DTM programme ran alongside GT and Formula E commitments that season as he transitioned from single-seaters to touring car and electric racing.
In August 2016, Rosenqvist was announced as Nick Heidfeld's partner at the Mahindra Formula E team for the 2016–17 season. He won his first Formula E race at the Berlin ePrix on 10 June 2017, which was also Mahindra's first Formula E victory. He remained in Formula E through the end of the 2017–18 season before departing for IndyCar.
Rosenqvist raced in the Super Formula series with Team LeMans in 2017 and moved to the Super GT series with the same team in 2018, replacing Andrea Caldarelli. These Japanese campaigns ran alongside his European and American commitments and broadened his experience across diverse racing disciplines.
Rosenqvist signed with Chip Ganassi Racing for the 2019 IndyCar Series season, his first full campaign in American open-wheel racing. He won the IndyCar Rookie of the Year award and finished sixth in the championship. He won his first IndyCar race in 2020 at Road America during the REV Group Grand Prix.
For 2021, he moved to Arrow McLaren SP, replacing Oliver Askew in the No. 7 car. A serious accident at the Detroit Grand Prix in June 2021 — caused by a stuck throttle — sent his car hard into the wall and required hospitalisation, though he escaped without life-threatening injury. He returned to form in 2022, picking up his first McLaren podium at Toronto, and in 2023 earned three pole positions at Texas, the IMS Road Course, and Laguna Seca, with a best race finish of second at Portland.
On 5 September 2023, Meyer Shank Racing announced Rosenqvist as their No. 60 Honda driver on a multi-year deal from the 2024 season. He immediately lifted the team's qualifying pace, taking pole at Long Beach in 2024 for Meyer Shank Racing's first ever IndyCar pole position. He finished twelfth in the 2024 championship standings. In 2025, he qualified in the Firestone Fast Six at Indianapolis and finished fourth in the race before following that with a second at Road America, finishing sixth in the season standings.
In 2026, Rosenqvist won the Indianapolis 500 in what was recorded as the closest finish in the race's history, beating David Malukas to the yard of bricks by 0.0233 seconds.
Rosenqvist has been identified as a street circuit specialist throughout his career. His pole positions and victories at venues such as Norisring, the Macau Grand Prix — where he won twice from pole — Long Beach, and the Grand Prix de Pau reflect an ability to extract pace from tight, unforgiving circuits where precision is paramount.
Rosenqvist's career exemplifies the modern multi-discipline driver: a dominant Formula 3 record across five European seasons, a DTM campaign, a Formula E win, Japanese championships, and sustained IndyCar competitiveness culminating in an Indianapolis 500 victory. His Formula 3 record — the most victories ever accumulated in the series — secured his place among the elite in European junior racing history even before his later American success.