Iannone's Pramac Ducati team-mate Ben Spies is already sidelined for the French Grand Prix as he continues to recover from lingering injuries.
Ducati test rider Michele Pirro will substitute for the American.
Regular MotoGP surgeon Dr Xavier Mir carried out Iannone's surgery in Barcelona on Tuesday.
Iannone told the official MotoGP website he was confident he would be fit enough to race at Le Mans.
"I feel good because Dr Mir has experience of this operation," he said.
"It is my first time but I feel very good.
"It have a little bit of pain but I'm focused on Le Mans."
The Italian admitted Le Mans might be tough for him, but felt it was worth having the operation mid-season so he could cope better with the rest of his rookie campaign.
"It will not be easy riding at Le Mans with this problem, but now it's possible that I'll be better for the future," said Iannone.