Midfielder Leandro Paredes and several Argentina players have received bans and fines for their part in clashes with Spain players at the World Cup final, Fifa said on Friday.
Argentina have also been ordered to play their next two home matches behind closed doors, though one match of that sanction is suspended.
Boca Juniors player Paredes will be banned for 10 international games and was fined $90 000.
He grabbed Eric Garcia by the throat and wrestled Spain's Gavi to the ground while holding his substitute's bib, which led to an escalation in the incidents after the final that Spain won 1-0 at MetLife Stadium in New Jersey on 19 July.
Paredes' Argentina teammate Nahuel Molina received a seven-match ban and must also pay a fine of $90 000, while Thiago Almada was suspended for one match and fined $30 000.
Gavi was handed a similar penalty for his part in the fracas.
The Argentinian Football Association (AFA) has been fined $321 000 for breaches of Fifa's disciplinary code relating to using a sports event for making demonstrations of a non-sporting nature, team misconduct, and discriminatory chants and gestures by its supporters.
After Argentina beat England 2-1 in a tense World Cup semifinal, several Argentina players held up a banner saying: "The Falklands are Argentine".
Argentine forces invaded the British overseas territory in the southwest Atlantic Ocean in 1982, which resulted in then-British prime minister Margaret Thatcher sending a naval task force to reclaim them.
The resulting conflict, which lasted for 74 days from April to June 1982, led to the deaths of 655 Argentine and 255 British servicemen. Three people from the islands also died.
The AFA said it would appeal the suspensions and fines.