But in a potential boost to United Kingdom brewers and vineyards, all 880 pubs - affectionately known as Spoons - will sell British sparkling wines and wheat beers instead.
The move was part of a review all products over the next six to 24 months, he said, adding: "We intend to honour existing contracts with European Union suppliers, some of which have several years to run".
Martin accused the EU customs union of being a "protectionist system" which is "widely misunderstood".
He said that he intends to find a replacement for prosecco from the United Kingdom or new world countries which include Argentina, Australia, Chile, New Zealand, South Africa and the US.
With French Champagne off the menu, Wetherspoon's customers seeking a glass of bubbly will be offered Denbies Sparkling Whitedowns Brut and Whitedowns Rose Brut as well as Hardys Sparkling Pinot Chardonnay, from Australia.
Wetherspoon said its new wheat beers brewed in the United Kingdom will include Blue Moon Belgian White, Thornbridge Versa Weisse Beer and SA Brains Atlantic White.
It will continue to serve Kopparberg cider from Sweden, after the firm confirmed that it will be producing its cider in the United Kingdom post-Brexit.
His comments came after the chairman of Sainsbury's, David Taylor, the British Retail Consortium and former Deputy Prime Minister Nick Clegg warned Brexit without an European Union trade deal will drive up food prices.
Martin has previously argued that if the United Kingdom ends tariffs and agrees to unilateral free trade, Wetherspoon's pints could be made cheaper.
However, we are starting to make the transition to non-EU trade now'.
Wetherspoon's will continue to serve Kopparberg cider from Sweden.
Alcohol-free Adnams Ghost Ship will replace Erdinger alcohol-free beer from Germany.
Martin has maintained - contrary to industry expert opinion - that Brexit can mean cheaper food for British customers.
"Champagne has lost market share to lower price sparkling wines", Mr Martin said.
So probably good news if you're a UK-based craft beer producer, or your dad's got a vineyard in Dorset.
He added the government should also cancel the £39billion Brexit bill, which he dubbed a "leaving gift", and invest the money on local projects.
Martin is a staunch Brexit supporter and has been vocal in his support of Britain's departure from the EU.