The decision drew criticism from several top golfers, including four-times major winner Rory McIlroy, and Muirfield was removed from the list of courses that host Britain's Open championship by tournament organisers, the Royal and Ancient.
With 64 percent of members voting in favour of admitting women in the first ballot, club captain Henry Fairweather felt a second vote would be a step towards restoring their damaged reputation.
"A substantial majority of our members voted for change and many have voiced their disappointment with the ballot result and with subsequent events," Fairweather said in a statement.
"The club committee believes that a clear and decisive vote in favour of admitting women as members is required to enable us to begin the task of restoring the reputation of the club that has been damaged by the earlier ballot outcome."
The decision to hold a second ballot was welcomed by the Women in Sport charity.
"It is hardly surprising Muirfield's reputation has been significantly damaged as it is clear they currently fail to offer an environment that is welcoming to all," it said in a statement.
"While we hope a re-vote will see their membership policies brought into line with gender equality expectations of the 21st century, ensuring women receive the full benefits of this sport should have been happening far sooner.
"We hope the members of Muirfield, who have been afforded a second chance on this issue, will not make the same mistake twice."
American Phil Mickelson won the British Open the last time it was hosted at Muirfield in 2013.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by John O'Brien)
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