Lionel Messi led the Argentine team to the locker room before kickoff after players approached the stands to try to calm things down.
Policemen on the scene used batons to break up the brawl between supporters of both teams, with Argentina telling their Brazilian rivals they would only return to the pitch after the situation was calm.
Brazil players remained on the pitch waiting for their rivals 20 minutes after the scheduled kickoff time.
All 69,000 tickets for the match in Rio de Janeiro were sold.
Police gathered around Argentina fans in a section that can host about 3,000 fans.
Argentina leads South American World Cup qualifying with 12 points in five matches. Brazil is in fifth position. Both teams lost their previous games in the round-robin competition of 10 teams.
The Associated Press contributed to this report.