"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 in doubt for his scheduled defence of the US PGA Championship title next month.
The 26-year-old Northern Irishman is the current world No 1 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, while at the US Open he was five shots back and finished tied ninth.
Former European Tour physio Jonathan Shrewsbury believes that McIlroy is facing a real struggle to be fit for the British Open, saying the normal recovery time was 12 weeks for the injury.
"Rory is really up against it to play in the Open," the Englishman explained. "He's going to have to walk around seven or eight miles a day.
"It's hard, a really hard links course, and that's going to take its toll.
"The other thing is the confidence of being able to hit through the ball. As he comes into the follow through he is going to be rolling his ankle over and that is going to pose significant challenges."
Shrewsbury, who worked for the European Tour between 1992-2001, now runs a centre on the outskirts of London helping a range of elite sports professionals.
While he believes McIlroy is unlikely to be fully fit to defend the Claret Jug, he said the golfer will benefit from having treatment morning, noon and night.
"It's a very, very common injury, many people go through this, from the weekend warrior to elite sports people. It's normally around a 12-week recovery."
"Rory may be a superman on the golf course, but he is going to heal pretty much at the same rate as anyone else."
