Atletico hit with partial stadium closure after racist abuse
The Spain international heard monkey chants directed at him in the first half of his team's 3-1 defeat at Atletico's Metropolitano stadium in Spain's top flight on Saturday.
"(Atletico have been issued) a sanction of partial closure of their sports venue for a period of two matches and a financial penalty of 20,000 euros (£17,000)," said the federation's competition committee in a statement.
One area of Atletico's stadium will be shut for the upcoming league matches against Celta Vigo and Osasuna, as they strive for a top four finish.
"I went to take the corner and I heard monkey noises," said Williams after Saturday's game.
"There weren't many of them. There are stupid people everywhere... I hope this changes bit by bit."
Williams scored after the abuse and celebrated by pointing to his arm in reference to his skin colour.
"(The celebration) was with a bit of anger, it's not normal to be insulted for the colour of your skin," he added.
Spanish football has suffered a spate of racist incidents in recent years, many of which have been aimed at Real Madrid forward Vinicius Junior.
The Brazil international earned global support after facing off with a fan who was abusing him last year at Valencia's Mestalla stadium, which also faced subsequent partial closure.