In the latest injury blow to the Lions management, the combative Munster hooker suffered a chipped bone in his left elbow during training on Wednesday.
A scan revealed Flannery requires surgery that will prevent him from departing for South Africa with the rest of the squad on Sunday.
He joins Ireland team-mates Tomas O’Leary and Alan Quinlan on the list of withdrawals, although Ulster’s Rory Best would increase their number if he is picked to replace Flannery ahead of Scotland’s Ross Ford.
Tom Croft will link-up with the party today after being summoned to replace the suspended Quinlan – with a second newcomer also set to join the squad.
England back row Croft was promoted last night after Quinlan’s appeal against his 12-week ban for eye-gouging was rejected.
Head coach Ian McGeechan is also considering his options after Leigh Halfpenny was told to temporarily remain at home to undergo intensive treatment on a thigh injury.
Halfpenny remains part of the squad and will join the Lions in South Africa once he has regained full fitness, but McGeechan will also name a replacement as cover on Thursday.
“Leigh’s injury will take longer than first thought and we have decided to only go with fit players,” said the Scot.
“You don’t want to be on tour not training or playing and he will get full medical attention in Cardiff.
“If the recovery goes as planned he we will join us as soon as he’s fit.”
England full-back Delon Armitage, Wasps’ retiring World Cup winner Josh Lewsey and Scotland’s goalkicking ace Chris Paterson are all possible alternatives.
Turning his attention up-front, McGeechan admits he sympathises with Quinlan but insists the rangier and more athletic Croft would offer a new dimension to the back row.
With just 11 caps Croft is still a Test rookie but the 23-year-old had a major impact in the latter stages of the Six Nations and was considered desperately unlucky to miss out on initial Lions selection.
“When you have a squad of 37 there are always going to be some close calls and Tom fit into that category,” said McGeechan.
“Tom brings speed and his line-out ability to the squad. We can look at developing his role in the back row. His presence is another string to our bow.
“I’m very disappointed Quinlan will have to miss out on a Lions tour but Tom is a young buck with a lot of talent. He gives us something different.”