The surgery will take place on Thursday. Spanish media reported that his recovery time will be between two and four months if the operation goes as planned.
Asencio, 23, has been battling injury since the start of the season and was not included in Real's matchday squads for their first five games.
He made 34 appearances for Real last season, but lost his starting place in the last three months of the campaign.
New signing Ibrahima Konate and Dean Huijsen have been coach Jose Mourinho's regular central defenders this season, and he can also call on German Antonio Rudiger.
Eder Militao continues to recover from the hamstring surgery that has kept him sidelined since April.