Davies was injured during Spurs' 2-1 home defeat by struggling West Ham United in the Premier League on Saturday.
The 32-year-old was given oxygen before being carried off on a stretcher 19 minutes into the game.
"We can confirm that Ben Davies will undergo surgery today for a fracture of his left ankle," Tottenham said on their website. "Following the surgery, Ben will commence his rehabilitation with our medical staff."
As well as another injury blow for Spurs, who are without several senior players ahead of Tuesday's home Champions League clash with Borussia Dortmund, the injury to Davies could be a setback for Wales as they bid to reach the World Cup.
They face Bosnia-Herzegovina in their World Cup playoff semi-final at Cardiff City Stadium on March 26th, with the winners at home to Northern Ireland or Italy on March 31st.