After Minassian had his motorsport career started in 1990 in karting, 1992, he was fifth in the French Renault Clio Cup. A year later, he became vice-champion of the French Formula Renault. Then he moved in 1994 to the French Formula 3 Championship. After he was sixth in the first season, he won the 1995 runner-up title in this series. Then Minassian left France and went two years in the British Formula 3 Championship. For Promatecme starting he took in 1997 after he was a year before finishing fourth in the standings, also the runner-up title this series.
In 1998, Minassian in the Formula 3000 and went for West Competition at the start. The Frenchman could not with his teammate Nick Heidfeld, who won the runner-up title match in his debut season and finished 13th in the overall standings. 1999 denied Minassian as a driver of Kid Jensen Racing its second season in Formula 3000th After four point-less race, he celebrated his first at Silverstone Formula 3000 victory. With two other podium finishes, he finished the season in sixth place overall. In his third season Minassian moved in 2000 to the top team supernova. The Frenchman won the race in Imola, Magny -Cours and Zeltweg. Minassian, who delivered himself with Bruno Junqueira a fight for the championship, eventually had to admit defeat and was second again a championship.
In 2001, Minassian to America in the CART series. When Chip Ganassi Racing teammate, he was his former Formula 3000 Rivalens Junqueira. In the new series, however, he could not keep up with Junqueira and he had already claimed six races his cockpit to Memo Gidley exits.
2002 Minassian returned to Europe. Although he started in a race to the World Series by Nissan, his main focus, however, was no longer on the Formula racing. He was sixth in the 24- hour race at Le Mans and also won the championship title of NASCAR, a British touring car racing series. 2003 Minassian returned once in the Formula 3000. His commitment, however, was already finished after a race because he of his team - was fired - Fire Motorsport. Minassian started again at the 24 - hour race at Le Mans and this time was ninth.
Since 2004, Minassian is active only in endurance racing. He launched since with various Le Mans prototypes in the 24 Hours of Le Mans and in the Le Mans Endurance Series. He also went on some race of the American Le Mans Series at the start. His most successful season denied Minassian 2008, when he was vice-champion of the Le Mans Series and second in the 24 - hour race at Le Mans. In 2009 he scored in the 24- hour race at Le Mans fastest lap.