The veteran suffered the setback in Tottenham's home defeat to West Ham.
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The operation was performed on Monday, with Spurs announcing: "We can confirm that Ben Davies will undergo surgery today for a fracture of his left ankle."
There has been no news on how long Davies will be sidelined, but the surgery puts his hopes of being part of Wales' World Cup playoff in jeopardy.
Wales face Bosnia-Herzegovina in the World Cup play-off semi-final at Cardiff City Stadium on 26 March, with the winners at home to Northern Ireland or Italy in the final on 31 March.