The La Roja supporters invaded the stadium after failing to secure tickets for the game on Wednesday evening, and the followers vandalised the area that housed the journalists who were covering the game.
A statement from FIFA read: "Ahead of the Spain-Chile match at the Maracana, a group of individuals without tickets violently forced entry into the stadium.
"The situation was brought under control quickly and at least 85 intruders were detained, according to the military police of Rio.
"The organisers of the FIFA World Cup condemn these acts of violence and will communicate further information and measures to be taken in due course."
The result means that World Cup holders Spain are eliminated from the competition.