Petri's family was Dutch, but he was born in Hanover in Germany and was brought up in Dresden. His father was a professional violinist who taught his son that instrument. Egon played in the Dresden Court Orchestra while still a teenager.
From an early age, Petri had also taken piano lessons and he eventually concentrated on that instrument. He studied with Ferruccio Busoni, who proved to be a big influence on him. Thanks to him, Petri focused on the works of Johann Sebastian Bach and Franz Liszt, composers that, along with Busoni himself, remained at the centre of his repertoire.
Petri moved with Busoni to Switzerland during World War I where he assisted him in editing Bach's keyboard works. In the 1920s Petri taught in Berlin, Victor Borge among his pupils. In 1923 he became the first non-Soviet soloist to play in the Soviet Union. In 1927 he moved to Zakopane in Poland. From 1929 he made a number of recordings.
With the outbreak of World War II, Petri moved to the United States where he worked first at Cornell University and later at Mills College in Oakland, California. Earl Wild was among his American students.
Petri died in 1962 in Berkeley, California.