O'Driscoll, who won two Test caps on his third Lions tour two summers ago, will be unavailable for this Saturday's clash with Scotland at Murrayfield and next weekend's match against France in Dublin.
"He's been doing 80% of the work over the last two weeks," said Ireland team manager Paul McNaughton.
"I'm not too concerned about him. He's got a problem with his shoulder/neck and he's been getting some traction on it.
"But he's making progress. He's doing everything except contact up to this week."
McNaughton is hopeful that the 32-year-old will return in time for the second of two back-to-back games with the French on August 20.
O'Driscoll would then also be in line to face England at the Aviva Stadium on August 27, two weeks before Ireland's World Cup opener against the United States on September 11.
However, with O'Driscoll and fellow first-choice centre Gordon D'Arcy both ruled out of the next two games through injury, head coach Declan Kidney is facing something of a midfield conundrum prior to the trip to Edinburgh.
D'Arcy and O'Driscoll started all five RBS 6 Nations games alongside each other earlier this year and can boast 169 Ireland caps between them.
With the veteran duo unavailable, Kidney has a number of options open to him but none can match the experience and understanding offered by D'Arcy and O'Driscoll.
Paddy Wallace is likely to start at inside centre against the Scots having seen just 11 minutes of international action so far this year, while Lions tourists Keith Earls, Tommy Bowe and Luke Fitzgerald could all be switched to outside centre if Kidney opts not to start utility backs Fergus McFadden or Gavin Duffy in the No13 shirt.