The Argentina football federation (AFA) was charged with crowd disturbances and the late kickoff at Tuesday's game in Rio de Janeiro.
The Brazilian federation was charged with failures of managing security at a game it organised, FIFA said.
Fights among fans broke out after the national anthems. The teams were led back to the dressing rooms and the game started 27 minutes late.
"There was family of the players [there]. We were more worried about that than playing the match," Argentina captain Lionel Messi said.
Argentina won the game 1-0.
FIFA gave no timetable to judge the case and impose sanctions.
Brazil and Argentina could next meet at the 2024 Copa América, a tournament that will be played in the United States from June 20 to July 14.