Born in Kazakhstan, Stravinsky began playing the violin at the age of four and was accepted into the Moscow Central Music School (affiliated to the Tchaikovsky Conservatoire) when he was six. He joined the rest of his family in London at the age of ten when he immediately made his British debut at a Leighton House recital and commenced studies under Lord Menuhin at the Menuhin School learning both violin and viola. Three years later, he became the first former Soviet student to secure a scholarship in music to Eton College. He then studied violin at the Royal Academy of Music in London, graduating in July 2002.

From the age of fourteen, Stravinsky participated in international European festivals. He received his conductor training from Igor Golovchin, Thomas Sanderling and Geoffrey Boyd, Claudio Abbado. Whilst being an undergraduate student, Stravinsky formed his own ensemble. They performed a wide repertoire of works including Haydn, Honneger, Shostakovich and many others. In September 2002, Stravinsky took up the position of assistant conductor to Vladimir Ponkin, Music Director of the Helicon Opera.

In 2004 Stravinsky made his operatic debut directing Helicon Opera with Carmen, Bizet. Marius Stravinsky performed with Lithuanian Chamber Orchestra, Belarus State Symphony Orchestra, Kuban Symphony Orchestra, National Orchestra of Malta, Royal Philharmonic orchestra and many others.