The winner of six Group One races on the track, he went on to become one of the world's leading stallions for the Coolmore Stud.
A statement from Coolmore said he died on Thursday morning after a short illness "which was due to complications from an overwhelming septicaemia".
The son of Sadler's Wells sired Derby winners Motivator (2005), Authorized (2007) and Pour Moi (2011).
Montjeu retired to stud at the end of 2000 after a racing career that saw him win the 1999 French and Irish Derbies, as well as the Prix de l'Arc de Triomphe the same year.
Mick Kinane, who rode Montjeu to five victories
“He's going to leave a big hole in racing”
Trained by John Hammond to win 11 of his 16 starts, he was also a brilliant winner of the 2000 King George VI And Queen Elizabeth Stakes at Ascot.
During his breeding career, Montjeu provided a succession of winners for the Coolmore team of John Magnier, Derrick Smith and Michael Tabor, in whose colours he raced.