McIlroy, the top-ranked golfer in the world, revealed the injury on his Instagram account Monday, saying he suffered it while playing soccer over the weekend.
"Continuing to assess extent of injury and treatment plan day by day,'' McIlroy wrote. ''Rehab already started.... Working hard to get back as soon as I can.''
Sean O'Flaherty, McIlroy's spokesman, told the Associated Press that the defending British Open champion would sit out this week's Scottish Open before making a decision on whether to play at St. Andrews on July 16.
In his Instagram post, McIlroy stated that he ruptured his anterior talofibular ligament, an injury that could make it difficult for him to shift weight while following through on a golf swing.
Along with Masters and U.S. Open champion Jordan Spieth, McIlroy was considered one of the favorites to win the British Open.
"That's a big blow to the Open if he misses it,” former Ryder Cup captain Sam Torrance said.
The Associated Press contributed to this report.