French police are looking into whether Benzema played a part in an alleged attempt to extort money from Marseille player Mathieu Valbuena.
The allegations center around a purported sex tape, a source close to the investigation told AFP.
Benzema was back in Madrid Thursday evening, where he trained and held a meetting with Perez, who "expressed his confidence that his actions were in good faith and that he is completely innocent."
"The club values and recognises the professional commitment, the displays of camaraderie with his teammates and the impeccable attitude he has shown as a core member of the first team squad for the more than six seasons that he has been a part of Real Madrid," added the Real statement.
Benzema is under investigation for "complicity in blackmailing and participating in criminal association with intent to organize a crime," according to a statement from the Versailles prosecutor's office.
The statement used the French term "mise en examen" -- a legal status that allows prosecutors to investigate someone accused of criminal activity for up to two years.
Benzema's attorney Sylvain Cormier says the 27-year-old has "taken no part in this blackmail attempt," and that the case has gone public "in a fallacious manner."
"His heart goes to his friend Mathieu Valbuena," Cormier said in a statement broadcast on BMTV.
Benzema appeared before a Versailles judge Thursday morning after being held overnight.
Prosecutors say he has received a probation order and is not allowed to contact Valbuena.
Both players were left out of the France squad for this month's friendly international matches Germany and England.
Benzema could also potentially miss the 2016 European Championship finals which will be held in France next June and July. He has represented his country on 81 occasions and was a key part of the squad for last year's World Cup in Brazil.
Valbuena did not immediately respond to CNN's request for comment.
Real, who top La Liga on goal difference, are away at Sevilla Sunday.