Flannery, who missed another tour last summer after fracturing an elbow while training with the Lions, suffered calf damage in Ireland's loss to the Barbarians on Friday night.
The 31-year-old sustained the injury after coming on as a replacement in the Thomond Park encounter which the Babaas won 29-23 after holding off a late Irish comeback.
Horgan failed to even make that match despite being named on the wing for the non-cap international.
The veteran wideman, who was part of the Leinster side beaten by the Ospreys in the Magners League Grand Final the weekend before last, has been struggling with a stomach complaint and was ruled out in the lead up to kick off.
Even if both players do get the go ahead to join their team-mates in New Zealand, neither will be considered for Saturday's Test against the All Blacks in New Plymouth.
"Jerry is getting a scan on Tuesday morning when the injury settles down and, depending on the results of that scan, he may join us," said Ireland team manager Paul McNaughton.
"If the scan is clear he'll be with us and he will travel on Tuesday but he won't be in consideration for this game.
"Shane Horgan is just continuing with some tests and we'll make a call on bringing him out on Tuesday or Wednesday at the latest and, again, he won't be considered for the All Blacks game."
Flannery's Munster understudy Damien Varley has been called up to the squad, as has Munster-bound wing Johne Murphy.
The Ireland squad arrived in New Zealand late last night, with rising star Jonathan Sexton among the party after fears that he too may miss the tour.
The young Leinster fly-half was another absentee from the Babaas match but has since recovered from an infection in his gum close to where he had recent surgery on his jaw.
Ireland are already without Paul O'Connell, Rory Best, Keith Earls, Kevin McLaughlin, Luke Fitzgerald, Denis Leamy and Fergus McFadden for their tour games against the All Blacks, the New Zealand Maori and the Wallabies later this month, but backs coach Alan Gaffney remains confident that his side will be able to compete Down Under.
"It was always going to be tough, but it's probably a touch tougher again," said Gaffney.
"But we are still confident with the squad we have out here at the present time. We're coming out here confident in our abilities but it's going to be a tough day at the office obviously and we fully understand that.
"We've come out here with what I still consider to be a strong squad even though we've left a lot of guys at home with injuries.
"That depth has been developed over a number of years now and is still going forward as far as we're concerned.
"There are a lot of young boys in their 20s now making their mark and could even be in consideration in 15 months time.
"It's started to make Ireland much more competitive when we suffer these injuries and we can replace them with very strong players."
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