"Total rupture of left ATFL (ankle ligament) and associated joint capsule damage in a soccer kickabout," McIlroy wrote on his Instagram account.
"Continuing to asses extent of injury and treatment plan day by day. Rehab already started...working hard to get back as soon as I can," he said, alongside a photograph showing him standing on crutches with his left ankle in a heavy surgical boot.
McIlory's showdown with double major winner Jordan Spieth was expected to be the highlight of the Open, which takes place at St Andrews on July 16-19.
McIlroy, who won last year's Open at the Royal Liverpool course, Hoylake, may also be doubtful for his scheduled defence of the US PGA Championship title next month.
The 26-year-old Northern Irishman is the current world number one and has won four major titles, the 2011 US Open, the 2012 PGA Championship and, in 2014, the British Open and the PGA Championship.
He is one of only three men, along with Jack Nicklaus and Tiger Woods, to have won three majors by the age of 25.
After a strong start to the 2015 season, he showed signs of fatigue when he missed the cut at two successive events in May and said that, after five successive tournaments, he needed to take a break.
McIlroy has injured his ankle playing football before. He suffered a similar, but less severe, problem in December 2013 after which he revealed: "I was off my ankle for about a week over New Year."
He was due to play in the Scottish Open this week as part of his preparations for the Open.
McIlroy was out of contention to win at the two majors won by Spieth this year.
At the Masters, in April, he was four strokes adrift and at the US Open he was five shots back and finished tied ninth.
(Editing by Toby Davis/Amlan Chakraborty)
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