O'Connell and Ferris have lost their battles with respective back and ankle injuries, ruling them out of the climax to the Guinness Series on Saturday week.
The Lions forwards' absence means Ireland will be without six key personnel against the Pumas, with Brian O'Driscoll, Rory Best, Rob Kearney and Sean O'Brien completing the list.
It is yet further bad news for Ireland, who were edged out 16-12 by South Africa on Saturday despite leading 12-3 at half-time.
Fiji are the next assignment - in a non-cap international at Thomond Park - but all eyes are trained on Ireland's meeting with Argentina, with defeat potentially dropping them into the third tier of seeds for the 2015 World Cup draw.
Ireland sank to eighth in the IRB's latest rankings, the gauge used to determine seedings for the 12 directly qualified teams for the tournament, which is being hosted by England.
For the Irish to plummet to ninth, results this weekend would have to go against them, with Scotland beating South Africa and Wales defeating Samoa.
Scrum-half Eoin Reddan, a substitute against the Springboks, will see a specialist this week after sustaining bruising to his ankle, so Ulster's Paul Marshall has been drafted into the squad.
Lock Donnacha Ryan and prop Cian Healy have passed mandatory concussion tests.
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The Barbarians are one of the top invitational rugby sides with a long history and classic rugby jersey.
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The Lions are ready to get their Australia tour underway. They arrive in Perth on Monday.
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The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.