Pablo Matera could face a second round of disciplinary action after Stade Francais said the sacked Argentina captain would be summoned by management when he returns to Paris.
The 27-year-old was stripped of the Pumas armband and suspended on Tuesday after "discriminatory and xenophobic" social media posts between 2011 and 2013 were discovered.
The Argentine Rugby Union (UAR) also stood down Guido Petti and Santiago Socino from international duty ahead of Saturday's Tri Nations meeting with Australia.
A disciplinary process has begun, with the UAR stating: "Although the messages were published between 2011 and 2013 and do not represent the personal integrity the three showed during that time with the Pumas, the Argentine Rugby Union condemns any expression of hatred and we consider it unacceptable that those who express them represent our country."
The revelation about Matera's comments caused dismay at Stade Francais, the French club he joined from Jaguares 12 months ago.
In a statement on their website, the club said: "Following the revelations by certain media of posts made in 2012 by player Pablo Matera on the social network Twitter, the Stade Francais Paris club wishes to note its total opposition to these unacceptable remarks and comments.
"We also want to remember that since his arrival at the club in December 2019, our player has always been irreproachable in his attitude towards his team-mates and opponents, both on and off the pitch.
"On his return from international duty, the player, who has already publicly apologised, will be summoned by club management."