Muirfield will not stage another Open Championship after maintaining its ban on women members in a vote described as "indefensible" and "embarrassing".
The Scottish club said voting in favour of allowing women had fallen just short of the required two thirds majority.
Governing body the R&A said it would not stage the Open "at a venue that does not admit women as members".
Scotland's First Minister Nicola Sturgeon said Muirfield's stance was "simply indefensible".
To admit women golfers as members, Muirfield - a privately owned links in East Lothian run by The Honourable Company of Edinburgh Golfers - needed two thirds (432) of its 648 eligible voters to back the move.
But after a "comprehensive" two-year consultation process described as "thorough" and conducted "with all due diligence and professionalism", it fell short.
Of the 616 members who voted, 397 - or 64% - voted for the resolution, while 219 (36%) voted against it.
Royal Troon is the only other Open venue that still excludes women. The club, which will stage this year's Championship, it is consulting members about altering that arrangement.
Muirfield last hosted the Open in 2013, when American Phil Mickelson won the Claret Jug.
Iain Carter, BBC Sport golf correspondent
"The Muirfield based Honourable Company of Edinburgh Golfers, have, at best, been left to look out of touch with modern thinking. At worst, they look like a bunch of selfish bigots who have no place at the top of the game.
"Sources close to the club suggest they will explore the opportunities of staging another ballot. One said they might ask for simple majority vote next time, instead of a two-thirds requirement.
"Another said overseas members might be allowed to take part in the decision-making process after being denied this time."
How have Muirfield reached this decision?
Muirfield captain Henry Fairweather, who announced the result of the ballot, said: "Our club committee recommended that members should vote for the admission of women as members.
"A majority voted for women as members but the two-thirds majority that we require for a change in the rules was not met. The club, therefore, will retain its men-only membership policy.
"The Honorary Club is a members club and the members decide the rules of the club, including its membership policy.
"Women will continue to be welcome on the course and in the clubhouse as guests and visitors, as they have been for many years."
A 33-strong group of 'no' campaigners among the Muirfield members had cited concerns about slow play and making women "feel uncomfortable" among the "risks" of admitting female members.
What has the reaction been?
English golfer Melissa Reid, twice a member of Europe's Solheim Cup team, described the decision as "embarrassing".
"You know it was an opportunity for Muirfield, but they've wasted it," she told BBC Radio 5 live.
"I think that the decision the R&A have made to postpone the Open being there is a good one. I wouldn't play there, because I'd be going against what I believe.
"We're still a long way off the men's game in terms of prize money, and this just sets it back even further".
R&A chief executive Martin Slumbers said: "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.
"If the policy at the club should change, we would reconsider Muirfield as a venue in future."
Scottish Golf said it was "disappointed" with Muirfield's decision.
"We believe every golf club has a duty to be inclusive and to reflect modern society. We hope that those who voted for change continue to make the case for the modernisation of their club," it added in a statement.
George Kerevan, the SNP MP for East Lothian, tweeted: "I'm outraged by decision of minority at Muirfield Golf Club to block admitting female members. Sad for golf, equality, democracy."
He added: "Defeat of proposal to admit women members at Muirfield Golf Club imperils the sport in East Lothian. Very selfish."