O'Leary joined Irish from Munster before the start of the season and made an instant impact combining with fly-half Ian Humphreys, but has not played since the Aviva Premiership defeat to Harlequins at the end of October.
The Exiles are currently 11th in the Premiership table, only six points clear of bottom club Sale Sharks, with scrum-halves Darren Allinson and academy product Jack Moates their two remaining options.
"London Irish scrum half Tomás O'Leary underwent a surgical procedure on his lower back last Tuesday (4th December) for a degenerative pre-existing injury that has deteriorated this season," said a club statement.
"Tomás has been unavailable for selection since his last appearance for London Irish against Harlequins at Madejski Stadium 28th October. He now faces four to six months lay-off."
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