After consulting with surgeons, it was decided Lukaku's best recovery option was "conservative therapy", which will see him out of action for "three to four months".
Both Lukaku and Napoli management are in agreement over the decision.
The Belgium centre-forward suffered the injury in preseason action against Olympiakos last week.
Napoli management have also decided against registering Lukaku for the Champions League group phase over the first-half of the season.