The suspension was decided during a meeting of the CSD executive committee in Madrid, after the Spanish administrative sports tribunal opened disciplinary proceedings against Villar.
The 67-year-old, a former acting president and current vice president of UEFA, which runs European football, has headed the Spanish federation since 1988.
The decision can be reviewed, according to the CSD spokesperson.
Villar's replacement is expected to be announced on Wednesday when the Spanish federation (RFEF) holds its general assembly.
Villar, who is also a senior vice president of FIFA, and his son Gorka were detained by police on July 18th in a series of early morning raids on federation headquarters and other sites as part of a fraud probe launched last year.
Also arrested were the federation's financial vice-president Juan Padron and Ramon Hernandez Baussou, general secretary of the Tenerife federation.
They face charges including falsifying documents, misappropriation of funds, collusion and administrative breaches linked to skimming profits from international friendly games and channelling the funds to Gorka Villar.
A Madrid court ordered Villar and his son Gorka to be held in custody on Thursday without bail following their arrest.
High Court judge Santiago Pedraz said there was a significant risk that the two men could make an attempt to flee the country given the seriousness of the crimes they are accused of and the "huge financial means" which they have.
Under Villar's watch Spain became one of the dominant forces in world football, winning two European Championships and the 2010 World Cup.
But his critics say his period in charge was marked by ethical issues and an autocratic management style.
Following his re-election in May for an eighth term, El Pais newspaper denounced his "despotic" management and bemoaned his close ties to FIFA and UEFA leaders embroiled in corruption probes.
The former Athletic Bilbao midfielder, capped 22 times for Spain, has been dogged by ethical issues over the years.
He was most notably fined 25,000 Swiss francs ($25,700) by FIFA's ethics committee in 2015 for failing to cooperate during an investigation into the awarding of the 2018 and 2022 World Cups to Russia and Qatar respectively.