After the hosts prevailed on penalties there were violent scenes as players and officials both clashed in the middle of the pitch.
"I am furious about that and our disciplinary committee will monitor this incident," Blatter told Britain's BBC Five Live radio station.
"We will take some steps towards those who are identified as being the provocateurs of this incident.
"There was really no need. After 120 minutes football is a drama and then you have to go to penalty kicks and then football becomes a tragedy, but one is the winner and one is the loser.
"What I always say is in football you learn to win, but you also have to learn to lose."
FIFA spokesman Markus Siegler confirmed that Slovakian referee Lubos Michel had shown Argentinean substitute Leonardo Cufre a red card for kicking German defender Per Mertesacker in the melee.
"Disciplinary proceedings against Cufre have been started because he received a direct red card," Siegler told reporters.
"The disciplinary committee will look at videos and will look into the matter."
Siegler admitted that FIFA "realised that a certain urgency was necessary" in investigating the matter due to Germany’s semi final with Italy on Tuesday.
TV pictures showed Argentinian defender Gabriel Heinze clearly trying to confront German team manager Olivier Bierhoff, but both men were restrained by players and officials.
"I was just trying to get in between the players," Bierhoff said. "I didn't want any of them to get in trouble and then be suspended.
"It is a pity. The fans in Germany have shown that they can interact in a friendly way, so players and team officials should set an example."
FIFA spokesman Siegler commented: "As far as we know, Oliver Bierhoff just tried to separate the players and prevent any altercation, but we will investigate."