The Northern Irishman picked up the stress injury in South Africa last week, the European Tour said.
McIlroy played with the injury for the final three rounds in Johannesburg, where he lost in a play-off to Graeme Storm.
The world-ranked number two behind Australia's Jason Day said it was "bitterly disappointing" to have to withdraw from a tournament he loved playing and "which is one of the best on the European Tour..."
He added: "In situations like this you simply have to listen to the experts and the team I have consulted have all advised me to rest until my rib has fully recovered."
Two of the world's top four players - Dustin Johnson and Henrik Stenson - headline the Abu Dhabi event alongside defending champion Rickie Fowler.
© 2019 dpa GmbH