Bale, 27, hobbled out of Tuesday's 2-1 Champions League win at Sporting Lisbon with what has been diagnosed as a "traumatic dislocation of the peroneal tendons" in his right ankle.
He will be operated on in London and is at risk of missing Wales' 2018 World Cup qualifier against Republic of Ireland in Dublin on 24 March.
That game is exactly four months away.
Chris Coleman's Wales are currently third in Group D, four points adrift of leaders Ireland and two points behind Serbia.
Bale extended his Real deal in October and is now tied to the Spanish giants until 2022.
He has made 20 appearances for club and country since August, scoring 11 goals.
Real Madrid forward Gareth Bale will have ankle surgery next Tuesday and is expected to be out for four months.