The band announced in May that dates would be postponed after doctors told the 52-year-old frontman to rest, after he damaged his voice during a performance at Cannes earlier that month.
Le Bon said in a statement: 'I need to take some more time away from shows to get back to full strength.
'If we knew exactly when that might be, we wouldn't have to let this entire run of dates go, but what we feel we can't keep doing is moving shows piecemeal, as it's just not fair on the fans.'
The group added that they are hoping to reschedule as many of the dates as possible.