O'Mahony was one of three key players injured in the 24-9 pool-topping win over France on Sunday.
Captain Paul O'Connell damaged his hamstring in the France game and has almost certainly played his last international but the Six Nations champions are more upbeat on flyhalf Johnny Sexton's damaged groin.
"Paul is in hospital awaiting a scan. Johnny suffered a groin injury and is awaiting a scan but we're hopeful," the IRFU said on Twitter.
Ireland are poised to call up lock Mike McCarthy to replace the 35-year-old O'Connell who is expected to be ruled out of the tournament on Tuesday, Irish media reported.
Ireland, who avoided any serious injuries before centre Jared Payne was sent home with a fractured foot on Saturday, lost O'Mahony in the second half of the hugely physical test when his foot got stuck in the grass and he twisted his knee.
Coach Joe Schmidt could face further back-row problems for the quarter-final against Argentina after Sean O'Brien was cited for striking France's Pascal Pape in the stomach.
O'Brien's hearing will be held on Tuesday. Ireland play Argentina in Cardiff on Sunday, bidding to reach the World Cup semi-finals for the first time.
(Reporting by Padraic Halpin, editing by Ed Osmond and)
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