The Honourable Company of Edinburgh Golfers, which owns Muirfield, announced its decision to retain the club's male-only policy following a ballot of its 750 members.

A two-thirds majority was required for a change to take place, but 36 percent of members voted against allowing women.

The R&A, which runs the British Open, said Muirfield has been taken off the list of courses that can host golf's oldest major championship.

Criticism of Muirfield's decision was led by Scotland's First Minister Nicola Sturgeon.

"Muirfield is a private club and they're in charge of their own rules and regulations, and I accept that, but this is 2016," she told BBC Scotland.

"Scotland has women leaders in every walk of life, in politics, in law, in business and everywhere else.

"I think this decision is wrong, and I hope there's a way of of looking at it again and overturning it.

"As well as being wrong, it's damaging to Muirfield as a club - I want to see the Open played at Muirfield, it's a fantastic golf course, so this really is a regrettable decision."

Muirfield is one of 10 courses on the British Open rotation and has hosted the event 16 times since 1892, most recently in 2013 when American Phil Mickelson lifted the trophy.

"Going forward we will not stage the Championship at a venue that does not admit women as members," R&A chief executive Martin Slumbers said in a statement.

"If the policy at the club should change, we would reconsider Muirfield as a venue for The Open in future."

Royal Troon, which hosts this year's tournament from July 14 until 17, is the only other club on the rotation to still exclude women.

Royal Troon Golf Club revealed earlier this week that it has written to its 800 members to canvas their opinion about whether they should change their policy. 

The Royal and Ancient Golf Club at St. Andrews, the spiritual "Home of Golf," opened its membership to women in 2014 for the first time in 260 years.

Royal St. George's, another British Open host, ended its male-only membership last year.

Augusta National, home of the Masters, decided in 2012 to invite women to join.

Henry Fairweather, captain of Muirfield, said the club had to follow the rules set by its members.

"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," he said.