Minardi grew up in Faenza in a family connected to the automotive trade. His father Giovanni managed a Fiat dealership and an Agip fuel station before his early death; the family later added Iveco and Selenia dealerships to their business interests. Giancarlo initially pursued a career in truck dealerships before turning his attention to motorsport.
He entered competitive driving in 1968 with a Faccioli-tuned Fiat 500, competing in hillclimbs with good results, before moving to rallying with a Fiat 124. He then took on a leadership role with the Scuderia del Passatore racing team, guiding it to runner-up honors in the 1972 Formula Italia championship and the title in 1973 with driver Giancarlo Martini. Following a rename to Scuderia Everest in 1975, the team contested the European Formula Two Championship with a BMW-March for two seasons.
In 1980, with financial backing from Italian motorsport patron Piero Mancini, Minardi formed the team bearing his name. The outfit spent four seasons in Formula Two before graduating to Formula One in 1985. A notable Formula Two result came in 1981, when Michele Alboreto won the Misano round for the team.
The Minardi Formula One team competed for two decades at the back of the grid, frequently hampered by limited resources. In 1991, Ferrari supplied the team with V12 engines. Financial pressure led to various changes in ownership structure: in 1994, Minardi joined forces with Scuderia Italia to keep the operation viable. By 1996 he had been compelled to sell 70 percent of the team to an investor consortium while retaining a minority stake. Flavio Briatore subsequently became the main shareholder in a deal brokered by Bernie Ecclestone, and in 1997 Gabriele Rumi of Fondmetal entered as a major partner; Minardi and Rumi shared the General Director role from 1997 to 2000.
In 2001, Australian businessman Paul Stoddart acquired the team, though Minardi remained as Managing Director with a focus on young driver development. He departed after Red Bull purchased the team and renamed it Scuderia Toro Rosso in 2006.
Minardi's most lasting legacy in Formula One is the number of future champions and race winners he introduced to the sport. Fernando Alonso, Giancarlo Fisichella, Mark Webber, and Jarno Trulli all made their Formula One debuts with the Minardi team. Following his departure, Minardi supported both the Minardi Team by GP Racing in Euro F3000 and Minardi Piquet Sports in GP2, with Nelson Piquet Jr. finishing runner-up to Lewis Hamilton in the 2006 GP2 championship.
Minardi has remained active in Italian motorsport administration. In 2021 he became president of the Imola Circuit, and in 2022 he was appointed President of the FIA's Single Seater Commission. His son Giovanni runs Minardi Management, a driver management firm whose clients have included Mercedes F1 driver Kimi Antonelli.
Minardi continues to live in Faenza, where he was also briefly chairman of football club Faenza Calcio and ran for Mayor of the city in 2010.