The European tour was due to kick off in Dublin next week and set to continue through mid-September.
Le Bon said he had damaged the muscles that control his vocal cords and he is unable to hit higher notes. He has been advised to undergo physical therapy.
The singer said it is unknown how long it will take for him to recover, but he added, "I am doing everything I can to work through this and get back on track as soon as possible."
Duran Duran became superstars in the 1980s with hits including "Wild Boys" and "Rio."
The band's latest album is the Mark Ronson-produced "All You Need is Now."
The Associated Press contributed to this report.