The Wales international picked up the injury during Tuesday's 2-1 Champions League victory at Sporting Lisbon.
"Real Madrid Sanitas Medical Services have decided that Gareth Bale will undergo an operation following the traumatic dislocation of the peroneal tendons of his right ankle," La Liga leaders Real said in a statement.
"The operation will take place at King Edward VII Hospital in London on Tuesday 29th November by doctor James Calder, under the supervision of the club doctors Jesus Olmo and Mikel Aramberri."
The 27-year-old winger has scored seven goals and set up three more in 16 starts for Real in all competitions this season.
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No time frame was given for his return to action.
Zinedine Zidane's team are four points ahead of Barcelona at the top of La Liga and play Sporting Gijon on Saturday.
(Reporting by Adriana Garcia, editing by Pritha Sarkar)
