It is reported that one of the players made the recording and shared it among team-mates on WhatsApp.
Madrid confirmed that a fourth player has also given a statement to police in a statement which read: "Real Madrid announces that it has learned that a Castilla player and three Real Madrid C players have given a statement to the Civil Guard in relation to a complaint for the alleged dissemination of a private video on WhatsApp.
"When the club has detailed knowledge of the facts, it will adopt the appropriate measures."
The players' identities have not been made public and El Confidencial claims that more players could be involved.
The alleged victim's mother reported the incident to police on September 6, sparking an investigation and the arrests on Thursday.
According to Relevo, recording a video without the victim's consent could be punished with one to four years in prison. However, if the victim is a minor, the range may increase to two to five years.