Tuesday's match in Rio de Janeiro's Maracana stadium, which world champions Argentina won 1-0, was delayed for around half an hour after rival fans started fighting before kick-off.
The iconic stadium descended into chaos, as players tried in vain to get fans to stop the fray. Argentina captain Lionel Messi led his team back to the dressing room, returning only after the violence had been quelled.
Police fought back the melee with batons, leaving some fans with bloodied faces and other injuries.
"FIFA can confirm that its Disciplinary Committee has opened proceedings against the Brazilian Football Association (CBF) and the Argentinian Football Association (AFA)," world football's governing body said in a statement.
Brazil face sanctions for "potential breaches of article 17" of FIFA's disciplinary code, which regulates order and security at matches.
Argentina, who inflicted the Brazilians' first-ever home defeat in qualifying for a World Cup, face sanctions for the "crowd disturbance" and "delayed kick-off".
The two teams risk fines as well as international home matches with partial or total closure of their stadium, the two most common sanctions.
Argentina are on top of the South American World Cup qualifying standings with 15 points from six games.
Brazil's third defeat of qualifying, meanwhile, leaves the five-time world champions in sixth place with seven points from six games.
