Matera will not be in the team to play Australia in the Tri Nations in Sydney on Saturday but his suspension has been lifted.
The flanker was stripped of the captaincy and among three players banned when “discriminatory and xenophobic” tweets resurfaced.
The posts from 2011 to 2013 were disparaging towards Black people, Bolivians and Paraguayans.
The Argentine rugby union (UAR) confirmed on Thursday that Matera, Guido Petti and Santiago Socino had faced a disciplinary hearing, where they had shown great remorse, and the ban had been lifted. However, it was agreed they wouldn’t face the Wallabies.
Centre Jeronimo de la Fuente will lead the team in Matera’s absence.
The Argentina team had suffered a huge backlash and Pumas coach Mario Ledesma said the players had suffered enough.
“They reached an agreement with the Union about not playing this game,” Ledesma said.
“It was really difficult and not a lot of sleep ... a lot of hate going on and they felt really affected and obviously the shame of what they did.”
Ledesma said the three players were “great men”, who no longer had the same views they had as teenagers.
“These three fine players and great men are great human beings; they have been suffering a lot this week, their families have been suffering a lot this week and it's really sad to see.
“Obviously they acknowledge what they did and are regretful and ashamed of what they did ... but what I can say is they are not the same people that they were at 17 or 18 years old.”
A UAR statement said: “The three players expressed their deep regret, reiterated the apology, ratified that it is not what they think and that it was a reckless act typical of immaturity.
“The disciplinary committee... understands that they have not repeated similar actions during these more than eight years, and that they have shown during this time to be people with firm and upright values, worthy of being part of our team.”