The proposal was submitted to Apple by the Central Laborers' Pension Fund in August. The fund owns nearly 11,500 shares, about a thousandth of 1 percent of the shares outstanding.
The proposal is on the agenda for the shareholders meeting on Feb. 23. Word of ISS's backing on Thursday comes two weeks after Apple CEO Steve Jobs announced he was taking his third medical leave since founding the company in 1976.
Apple's board recommends voting against the plan, saying it already has a succession plan in place, and that to reveal who it was considering for advancement could prompt rivals to poach its executives and cause others to leave.