O'Sullivan is already without a number of players, including captain Brian O'Driscoll, for the visits of New Zealand, Australia and Romania to Lansdowne Road.
Lions lock O'Connell, who started all three Tests against the All Blacks during the summer, requires surgery on his left hand, which he damaged in his seasonal debut against Llanelli last month.
The 26-year-old had the plaster removed from his hand on Tuesday and, following an examination, it was decided the injury had not healed sufficiently.
Surgery will rule the Limerick man out for three-to-five weeks, though there will be no lock replacement.
Meanwhile, Sheahan, who scored a try in Munster's European Cup defeat by Sale last Friday, has damaged neck ligaments and has been ruled out of rugby for six to 12 weeks.
A replacement for hooker Sheahan will be named on Sunday following the second round of pool matches in the European Cup.
It is a badly-timed blow for the 29-year-old, who was an unused replacement against the All Blacks in November 2001.
Sheahan has started just four Tests in the last three years because of the form of the now retired Keith Wood and new Saracens number two Shane Byrne.
O'Connell and Sheahan join O'Driscoll (dislocated shoulder), Denis Hickie (dislocated fibula), Alan Quinlan (cruciate knee ligaments), Guy Easterby (broken jaw) and Eric Miller (bruised ankle) on the sidelines.
Llanelli skipper Simon Easterby is currently nursing a broken nose and faces a fitness test.