The ANFP did not give details of the fine but said it would be sanctioned far more harshly if Chilean fans are involved in any other incidents.
Another investigation is ongoing after fireworks were set off during Chile's 3-1 victory over Australia in their opening Group B game.
"Yesterday (Monday) we got notice from FIFA's disciplinary commission that the Federation was being sanctioned with a fine for the incidents carried out by" Chilean fans, who pushed down a perimeter fence outside the Maracana and allowed about 200 supporters to rush into the media center," the ANFP said in a statement.
Brazil will beef up policing for World Cup matches at the Maracana stadium to try to prevent a repeat of the security breach, police officials in the country said on Friday.
"If a third case is opened by the FIFA for new incidents in upcoming games, the sentence could be very hard and harsh for (our) economic and sporting interests," the Chilean federation said.
The ANFP has said the fans involved in storming the Maracana will be punished at home by being banned from entering stadiums in Chile.
Chile have reached the World Cup last 16 and play hosts Brazil on Saturday in Belo Horizonte.   


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