The course last hosted the competition in 2013
Muirfield will not host an Open Championship until women are allowed become members of the club.
The news comes after it was revealed that a postal vote of members failed to reach the two-thirds needed to allow women join the club. Owned by the Honourable Company of Edinburgh Golfers, women can play on the course but remain forbidden from joining the club.
Phil Mickelson is the last player to win at the course. The American won in 2013, beating Henrik Stenson by three shots. Previous winners at Muirfield include Ernie Els, Nick Faldo, Tom Watson, Lee Trevino, Gary Player and Jack Nicklaus.
R&A statement on the announcement at Muirfield: Going forward we will not stage @TheOpen at a venue that does not admit women as members.— The R&A (@RandA) May 19, 2016
The R&A had not scheduled Muirfield to host another event between now and 2019, but it was expected that the tournament would have returned to the links in the next ten years.
Muirfield is one of the most famous courses in the World. It has previously hosted the Ryder Cup, the Senior's British Open and the Amateur Championship.
The Open will return to Royal Troon this year for the first time since 2004.