Matera has been punished for tweets that he posted between 2011 and 2013, in which he spoke of “running over blacks” with his car and also made disparaging comments about Bolivians and Paraguayans.
Two of Matera’s teammates, Guido Petti and Santiago Socino, have also been suspended for two weeks for similar reasons.
"The Argentina Rugby Union (UAR) forcefully rejects the discriminatory and xenophobic comments published by members of the Pumas squad on social media," a statement read.
The UAR board said it "repudiates the discriminatory and xenophobic comments published by members of the Los Pumas team on social networks."
It said the board resolved to "first, revoke the captaincy of Pablo Matera and asked (the national team) staff to propose a new captain to the board.
"Second, order the suspension Pablo Matera, Guido Petti and Santiago Socino from the national team until resolving disciplinary actions.
"Third, open a disciplinary case to the three players mentioned, which will be handled by the disciplinary commission of the Argentine Rugby Union."
The move comes fewer than three weeks since Matera led Argentina to their first ever victory over New Zealand, and means the trio will miss the final Tri-Nations match against Australia this weekend in Sydney.
Both Matera and Socino have issued public apologies for the posts, which have since been deleted.
"Today I have to take (responsibility) for what I said nine years ago. I am very ashamed,” Matera said on Instagram after deactivating his Twitter account.
"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.”
Socino added in a statement: "I want to apologise to those who I may have offended with what I said at the time, and what I absolutely repudiate. I never realised what it could cause, and I do not seek to justify it with the immaturity with which I handled myself."
The scandal comes in a week where Matera has already been forced to apologise for the “disappointing” tribute towards Argentine football great Diego Maradona, who died last week at the age of 60.
The Pumas squad wore black armbands for the heavy 38-0 defeat by the All Blacks on Saturday, whereas their opponents displayed a more moving tribute as captain Sam Cane laid down a New Zealand shirt with Maradona’s name and number printed on it before their traditional Haka.
Matera had admitted that "the tribute we chose to pay Diego caused pain and disappointment in many people and we wanted to (say) that in no way was that our intention.
"Diego was an extremely important person for us, he always supported us," Matera said, adding that "for Argentine athletes, Diego Maradona is the greatest thing there is and he marked us all."