Eugen Indjic made his first public performance at the age of nine, appearing with the Springfield Youth Orchestra in Mozart's Piano Concerto No.20. After two years, Mrs. Stephani introduced her young pupil to Alexander Borovsky, the eminent Russian pianist, who taught him in the Boston University for 5 years(1959-1964).

Between 1961 and 1969, invited by Arthur Fiedler, Eugen Indjic appeared numerous times each season with the Boston Pops Orchestra. His first concert tour (consisting of 13 concerts) was in Denmark (1963), together with Alexander Borovsky. "He plays Chopin as a pole, Debussy as a Frenchman and Prokofiev as a Russian master", wrote the Politiken of Copenhagen.

After his graduation in 1965 from Phillips Academy Andover, Erich Leinsdorf invited him to play Brahms' Piano Concerto No.2 with the Boston Symphony, making him the youngest soloist ever to appear with that orchestra.

"Leonard-Bernstein Scholar" at Harvard University, he studied musicology and composition with Laurence D. Berman and Leon Kirchner, graduating "cum laude" in 1969. Leonard Bernstein qualified him as "an extraordinary pianist and musician" and Emil Gilels, who often heard him during his American tours in these years, called him "a unique and inspired artist".
While in Harvard, he also took private lessons at the Juilliard School with Mieczyslaw Munz]] and Rosina Lhevinne's apprentice Lee Thompson.

In 1968, he met Arthur Rubinstein, who remained a friend and mentor until his death, calling Indjic "a world-class pianist of rare musical and artistic perfection". He studied composition with Nadia Boulanger in Paris and then definitely settled in France in 1972 after marrying Odile Rabaud, granddaughter of the French composer Henri Rabaud, who succeeded Faure as director of the Paris Conservatory, and coincidentally in 1919 the first French conductor of the Boston Symphony.

Prize-winner of three international contests - Chopin Competition Warsaw(1970), Leeds International Pianoforte Competition(1972), and Rubinstein Tel Aviv(1974) - Indjic has performed with the leading orchestras of the United States, Europe and Asia, and under such conductors as Leonard Bernstein, Vladimir Fedoseyev, Valery Gergiev, Eugen Jochum, Rafael Kubelik, Erich Leinsdorf, Kurt Sanderling, Giuseppe Sinopoli, Georg Solti, Edo de Waart and David Zinman, among others.
He continues to play regularly on great world stages such as Carnegie Hall Isaac Stern Auditorium, Avery Fisher Hall, Queen Elizabeth Hall, the Concertgebouw Grote Zaal, the Musikverein, Salle Pleyel and Theatre des Champs Elysees, Moscow Conservatory Bolshoi Hall, La Scala.

Eugen Indjic was invited to participate in a televised co-production (France, Poland, Japan) of Chopin's complete works and has recorded for Polskie Nagrania Muza, Columbia Records, RCA Victor, Claves and Calliope.

His discography includes works by Chopin (Piano Concertos, complete Ballades, Scherzi, Impromptus, Sonatas and Mazurkas), Debussy, Schumann, Prokofiev, as well as Beethoven. Arte Nova Classics has released live performances with the Suedwestrundfunk Orchestra of Tchaikovsky's Piano Concerto No.1 Concerto with Yuri Ahronovich and Rachmaninoff's Rhapsody on a Theme of Paganin with Sinopoli. His recording of Chopin's Mazurkas was doubly acclaimed because of the Joyce Hatto hoax. The English pianist signed her name to this disc and received rave reviews.

In addition to performing, Indjic regularly teaches master classes in Europe, Japan and the United States, and is a frequent jury member of international competitions including the Chopin Competition, Liszt Wroclaw, Rubinstein Tel Aviv, Prague Spring Festival, Lisbon Vianna da Motta International Music Competition.

In 2010, he was named "artist-in-residence" at the Prague Symphony Orchestra.