Supporters have complained in recent weeks that the same clubs are being made to play on Monday nights, with attendances at those games suffering as a result.
"There will no more football on Mondays," Rubiales wrote on Twitter.
"Starting from next season, there will be football on Saturdays and Sundays. We will see about Fridays, if we can reach an agreement that suits everyone.
"Business is important but more important are the fans."
La Liga has staged fixtures on Mondays since 2010 but clubs like Real Madrid, Barcelona, Atletico Madrid and Sevilla are not included, due to their involvement in European competitions.
The Spanish football fan group, FASFE, expressed its satisfaction at the announcement on Twitter. "Very good news for fans that like to support their teams from the stands," it read. "We appreciate the RFEF's stance on this matter."
There have been protests in recent weeks, with some fans that attended the game between Rayo Vallecano and Leganes last month turning their back on the pitch between the 10th and 12th minutes.
A week later, supporters refused to enter the stadium for the match between Alaves and Levante until five minutes after kick-off.