The four-time major champion, who lost to Englishman Graeme Storm on the third playoff hole at Glendower Golf Club, will start a rehabilitation programme for the stress fracture.
"To be forced to miss this week through injury is really quite annoying to be perfectly honest, but I am sure the tournament will be a huge success and I hope everyone involved has a great week," McIlroy said in a European Tour statement.
“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.”
The Abu Dhabi event, the first on the European Tour's Desert Swing, includes three 2016 major winners - Danny Willett, Dustin Johnson and Henrik Stenson - plus holder Rickie Fowler.
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(Writing by Ken Ferris; Editing by Frank Pingue)
