The 16-year-old stallion will be best remembered for his victories in the 1999 Prix de l'Arc de Triomphe and French and Irish derbies. He also won the King George VI and Queen Elizabeth Diamond Stakes at Ascot in 2000.
Montjeu, who triumphed in six Group One races, was retired to stud at the end of 2000. He sired 2005 Epsom Derby winner Motivator, 2011 champion Authorized and French raider Pour Moi, last year's winner.
"He was a really outstanding racehorse," jockey Mick Kinane told the BBC.
"That King George win was pretty good. He treated them with contempt that day and it was just a privilege to be on board.
"He had an aura about him ... and the great horses he's sired have all had that as well, that's what's made them great."