Saturday's game was halted after 13 minutes as fans repeatedly threw paper planes and rubber balls onto the pitch in protest against club owner Raul Martin Presa.
The committee ordered Rayo to close the south stand for their next home league match, against Elche on October 24th.
It warned that any repeat of similar incidents could result in the entire stadium being closed.
LaLiga has yet to announce when the match against Athletic will resume.
Protests against Presa have become increasingly frequent, fuelled by anger over what supporters regard as the neglect of the club's facilities.
Rayo's players and coaching staff issued a statement in February saying the training complex and home pitch were not fit for purpose. Madrid's regional government later suspended the club's use of Vallecas stadium over safety concerns, forcing Rayo to stage their first three LaLiga home games this season elsewhere.
Rayo disputed suggestions that the stadium was unsafe, saying technical inspections and two audits had found it met the required safety and public-health standards.
Presa told Cadena Cope last month that Vallecas stadium was in "optimal condition" and fans were not at risk.
Rayo said on Saturday that it would identify and punish those responsible for the disruption during the Bilbao game, accusing the group behind the protest of conducting a sustained campaign against the club.
Rayo are 13th in LaLiga with eight points. Their next match is away to Getafe on Monday.