Muirfield has been removed from the Open rota after members of the Honourable Company of Edinburgh Golfers (HCEG), which owns and runs the club, voted against admitting women members.
A two thirds majority of those who voted was required to change the club's membership policy, but 64 per cent voted in favour and 36 per cent against.
R&A chief executive Martin Slumbers said in a statement: " We have consistently said that it is a matter for the Honourable Company to conduct a review of its membership policy and that we would await their decision.
"The R&A has considered today's decision with respect to The Open Championship. The Open is one of the world's great sporting events and going forward we will not stage the Championship at a venue that does not admit women as members.
"Given the schedule for staging The Open, it would be some years before Muirfield would have been considered to host the Championship again. If the policy at the club should change we would reconsider Muirfield as a venue for The Open in future."
HCEG captain Henry Fairweather said: "The Honourable Company is a members club, and, as such, the members decide the rules of the club, including its membership policy. Women will continue to be welcome at Muirfield on the course and in the clubhouse as guests and visitors, as they have been for many years."
Muirfield last staged the Open in 2013, when it was won by Phil Mickelson.
Scotland's First Minister Nicola Sturgeon described the decision as "simply indefensible".
She tweeted: " Scotland has women leaders in every walk of life. It is 2016. This is simply indefensible."