The Open will no longer be hosted at Muirfield because the club's members have voted against admitting women members.
The Scottish club has been removed from the roster of clubs which host the tournament after the vote to remain a male-only club.
Golf's governing body, the R&A, has said it will not stage the competition at a course that does not admit women as members.
Chief executive Martin Slumbers said in a statement: "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."
The East Lothian club has been conducting a review of its membership in a two-year consultation process.
A two-thirds (66%) vote was needed to change the club's membership policy but the move failed by 2%
Muirfield club captain Henry Fairweather announced the result of the ballot.
He said the club's committee had recommended that women should be admitted as members, and he was "disappointed" with the decision.
However, he said: "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."
Members opposed to the vote have been criticised for claiming that their "foursomes and speedy play would be endangered" if women joined the club. In an unsigned letter seen by The Scotsman, members behind the 'no' campaign claimed:
:: Any woman member would be "bound to feel uncomfortable" and placed in an "unenviable, if not impossible, position" if they are "trickle fed".
:: It would take "a very special lady golfer" to be able to do the things expected of them.
:: The level of female membership may not meet the "standard" held by the club.
Scotland's First Minister Nicola Sturgeon described the decision as "simply indefensible" on Twitter, saying: "Scotland has women leaders in every walk of life."
East Lothian MP George Kerevan said the vote was "utterly selfish". He has written to the club asking it to hold a second ballot.
Muirfield and Troon were the only clubs on the 10-strong Open rota that had a male-only membership policy, though Troon shares its facilities with a separate ladies' golf club.
St Andrews voted to end its male-only membership policy in 2014, while Royal St Georges voted last year to admit female golfers with 90% of its members voting in favour of the move.
Muirfield is the world's oldest recorded golf club and has hosted The Open 16 times.
It last staged the tournament in 2013 and the R&A has said it could be considered again in the future if it changes its policy.