The club said it would take any appropriate action once it had "detailed knowledge of the facts"
The players were questioned and released after the data on their mobile phones was seized.
It follows a complaint filed in the Canary Islands by the mother of a 16-year-old girl who appears in the video, police said.
The players were arrested at the club's training complex on Thursday.
The club said it would "take appropriate measures" once it had "detailed knowledge of the facts".
Three of the players are from Real Madrid's C team, with a fourth coming from the club's B team, known as Castilla, it added.
"They were detained on suspicion of distributing a video with sexual content involving a minor," a Guardia Civil spokesperson said.
They added that while the girl said any acts were consensual, the recording was made without her consent.
The video was then allegedly shared via WhatsApp.
-- Courtesy of BBC Sport