The 85 times-capped Ireland international sustained the injury in Saturday's 23-21 victory in the first Test at Suncorp Stadium and the extent of the problem was revealed after further assessment.
A tweet from the official Lions Twitter account read: "Paul O'Connell ruled out of Test series with undisplaced fracture of lower rgt arm".
Arguably the Lions' most influential forward, O'Connell had been an integral part of head coach Warren Gatland's plans as they head to Melbourne 1-0 up.
The 33-year-old is on his third Lions tour, having played in seven Tests, and acted as captain back in the 2009 series against South Africa.
England forward Geoff Parling, who is due to skipper the Lions in Tuesday's game against the Melbourne Rebels, would be the obvious replacement.
Ireland prop Tom Court, currently in his home city of Brisbane, will join the squad on Monday as cover for Alex Corbisiero, who has a tight calf muscle.
Court will go straight on to the Lions bench for Tuesday's game.