Inbal was born in Jerusalem. He studied violin at the Israeli Academy of Music and took composition lessons with Paul Ben-Haim. Upon hearing him there, Leonard Bernstein endorsed a scholarship for Inbal to study conducting at the Conservatoire National Supérieur de Paris, and he also took courses with Sergiu Celibidache and Franco Ferrara in Hilversum (the Netherlands). At Novara, he won first prize at the 1963 Guido Cantelli conducting competition.
Inbal made most of his early appearances in Italy, but a successful British debut in 1965 with the London Philharmonic Orchestra led to a number of other engagements with British orchestras (he eventually took joint British citizenship). He subsequently worked with a number of orchestras throughout Europe and in America.
From 1974 to 1990 he was the principal conductor of the Frankfurt Radio Symphony Orchestra. With them, he was the first to record the original versions of several of Anton Bruckner's symphonies, for which he won the Jahrespreis der deutschen Schallplatten-Kritik. From 1984 to 1989 he was chief conductor at La Fenice in Venice.
Inbal has conducted a wide variety of works. He is best known for his interpreatations of late-Romantic works, but is also noted as an opera conductor, and has given the premieres of a number of modern works.