The 27-year-old and team-mates Guido Petti and Santiago Socino were suspended for racist comments posted on social media between 2011 and 2013.
Matera was reinstated two days later at the beginning of December.
But the Argentine Rugby Union now says his captaincy is contingent on the completion of an educational programme.
The UAR had previously said suspension was "unnecessary", describing the social media posts as "imprudent and immature".
But, following what the union calls a four-week "exhaustive investigation process". a statement said "the damage caused" by the posts "must be remedied".
"All racist, xenophobic and discriminatory comments are categorically condemned," the statement continued.
In order to be eligible for future selection Matera, Petti and Socino must participate in a six-hour course to learn how prejudices arise and the consequences these can have.
They must also record a video with educational content about discriminatory and prejudiced stereotypes which will be used as a teaching resource for players, then spend two days sharing their experiences on this topic as part of a course.
The union added: "The UAR will monitor the fulfilment of these activities to resolve the question of eligibility for future participation in the national side and/or eligibility to captain the side, questions that will be resolved in their own time.
"The eligibility of the three players remains subject to the fulfilment of the imposed restorative measures and Pablo Matera's captaincy is not guaranteed until the restorative measures are satisfactorily fulfilled."