Ma was born in Shanghai. His father owned a car repair shop, and the family channelled financial resources into supporting Ma's progression through motorsport. He began karting at the age of eight, and the family later invested in a karting track in Quyang to support his development. Ma won the national karting junior championship at the age of twelve.
Ma launched his professional career in the 2005 Asian Formula Renault challenge with Asia Racing Team, competing in six races and achieving a best finish of fifth. He also entered a single race in the 2005 Italian Formula 3000 championship and raced in the 2006 Formula Renault 2.0 NEC championship. He represented Team China in the inaugural A1 Grand Prix season at the Shanghai International Circuit, finishing seventeenth. Over the following years he raced in European Formula 3, including the 2008 Spanish Formula 3 Championship and the 2009 British Formula 3 Championship.
In April 2012, Ma was added to the HRT F1 driver development programme, becoming the first China-born driver to participate in a Formula One car at an FIA-sanctioned event. He replaced Narain Karthikeyan in the first Friday practice session of the 2012 Italian Grand Prix and was given three further Friday outings that season. He had a contract to race full-time for HRT in 2013 — which would have made him the first ever Chinese Formula 1 driver — but the team collapsed at the end of 2012.
Ma moved to Caterham for 2013, continuing as a Friday practice driver while racing in their GP2 Series team. At the 2013 Chinese Grand Prix he replaced Charles Pic in FP1, becoming the first Chinese driver to participate in a Formula 1 session at his home grand prix.
Ma made his GP2 debut at the 2013 Sepang round for Caterham. He suffered from gastroenteritis during the featured race, leading to extreme dehydration; he was diagnosed by the medical team on track and did not start the sprint race.
Ma joined the Citroën Total WTCC lineup for the 2014 season, driving at selected rounds as a fourth car entry. At the Race of Russia, he won the second round, making him the first Chinese driver to win a race in an FIA World Championship. He also posted the fastest lap at the Race of China in Shanghai, finishing thirteenth in the championship. Given a full-time seat for 2015, Ma won the second round of the Race of Portugal and finished fourth in the drivers' championship. He was not retained for 2016.
Ma entered Formula E in 2016, replacing Salvador Duran at Team Aguri for the final rounds of the 2015-16 season. He then signed with TeCheetah for the following season but was replaced by Esteban Gutiérrez after a difficult start. He made additional one-off appearances for the Nio Formula E Team in 2017 at Paris and New York, and returned full-time with Nio 333 FE Team in 2019. Travel restrictions prevented him from competing at the Berlin rounds that year, and he was not renewed for the 2020-21 season.
Ma competed in the 2020 TCR China series in a Lynk & Co 03 TCR. At the Guia Race of Macau, he finished second in the qualifying race of the season finale to secure the TCR China drivers' title. He subsequently joined reigning world champions Lynk & Co Cyan Racing in the 2022 FIA World Touring Car Cup and has continued racing in the TCR World Tour.
Ma Qinghua's career represents a significant chapter in Chinese motorsport. His FP1 appearances for HRT and Caterham opened doors as a pioneering figure at Formula 1 level, and his 2014 WTCC victory in Russia stands as a landmark moment — the first time a Chinese driver had won a race in an FIA World Championship. His sustained success in touring car racing demonstrated that his barrier-breaking achievements were grounded in genuine competitive ability.