Argentina coach Mario Ledesma said the side felt "disrespected" after photos of the Australia, New Zealand and South Africa captains were published.
Rugby Australia and governing body Sanzaar said a "late travel change" meant Julian Montoya could not attend.
Sanzaar said it was a communications breakdown and accepted responsibility.
"Sanzaar and Rugby Australia management would like to apologise to Argentina Rugby for the error that led to a photograph being published in the media that misrepresented The Rugby Championship in that it omitted Argentina," a statement said.
"Unfortunately, a late travel change then meant that the Argentina captain could not make the designated time for the photo session."
Argentina have lost all five of their matches in the tournament, with New Zealand sealing the title after beating South Africa on Saturday.
The Pumas are the only side which has played all its fixtures away in Covid-19 bubbles, with Ledesma saying earlier in September that his squad had not had enough time to prepare and "no-one seems to care" about his players' welfare.
Argentina's final match is against Australia on Saturday.