The sacking comes after revelations that the players had made racist comments on social media between 2011 and 2013.
Pablo Matera has been stripped of the Argentina captaincy and suspended, along with teammates Guido Petti and Santiago Socino, for posting racist comments on social media.
The Argentine Rugby Union (UAR) said on Tuesday its board had met urgently after revelations that the players had made racist comments on social media between 2011 and 2013.
The team said that although the posts were old and did "not represent the personal integrity that the three have shown during their current period with the Pumas," action had to be taken.
"The Argentine Rugby Union strongly repudiates the discriminatory and xenophobic comments published by members of the Los Pumas squad on social networks," the UAR said in a statement.
"Although the messages were expressed between 2011 and 2013 ... the Argentine Rugby Union condemns any expression of hatred and we consider it unacceptable that those who express them represent our country."
In his tweets, since deleted, Matera spoke of "running over blacks" with his car and disparaged Bolivians and Paraguayans.
The posts, mostly tweets, reportedly were aimed at Black people and Bolivian and Paraguayan domestic workers.
Matera has closed his Twitter account and expressed regret over the messages on Instagram.
“Today I have to take [responsibility] for what I said nine years ago,” Matera said. “I am very ashamed. Apologies to all those who were offended by the atrocities I wrote. At that moment I did not imagine who I was going to become.
"I’m also sorry to my team and my family for the moment they are going through ... and thanks to the people who love me for their support.”
The UAR said it had requested Pumas staff propose a new captain to the board and have the players stood down pending a "disciplinary process."
A team spokesman said the Pumas had cancelled all planned media activities on Tuesday and referred Reuters to the UAR's statement.
The scandal has thrown the Argentina camp into crisis days before their final Tri-Nations match against Australia in Sydney on Saturday.
Coach Mario Ledesma's side were thrashed 38-0 by the All Blacks on Saturday, a major reversal from their breakthrough 25-15 win over the New Zealanders in their opening match of the Tri-Nations last month.