The RFEF Disciplinary Committee also handed captain José Luis Gayà a one-match ban after his straight red card for a challenge on Kylian Mbappé during the second half.
The punishment for Vázquez follows the account provided by referee Francisco José Hernández Maeso in his match report. He stated that the Valencia director confronted assistant referee Iván Massó in the tunnel while repeatedly protesting against a foul decision.
According to the referee's report, Vázquez approached the assistant in an agitated manner, shouting: “It's not a foul, it's not a foul! Unbelievable!”
Hernández Maeso also reported that Vázquez continued making the same complaints when he passed the official. Police officers were required to intervene, identify the Valencia director and move him away from the area to bring the incident to an end.
The confrontation followed a decision to award a free-kick against Pablo Maffeo for a challenge on Mbappé. Although the subsequent set-piece was blocked by the Valencia wall, the ball fell to Fede Valverde, who scored Real Madrid's opening goal.
As reported by AS, Vázquez's suspension will keep him away from the pitch, dugout and dressing-room areas for Valencia's next two fixtures, against Rayo Vallecano and Osasuna.
The restrictions also prevent him from occupying the immediate vicinity of the bench or passing instructions to those involved in the match. The punishment includes a financial penalty.
Gayà, meanwhile, will miss the trip to Rayo after being sent off for his challenge on Mbappé. The disciplinary committee classified the incident as serious foul play, resulting in a one-game suspension.
Valencia therefore face their next league fixture without their captain, while Vázquez will also be unable to carry out his usual matchday duties for the following two games.