Ulster's other injury concerns Paddy Wallace, Pedrie Wannenburg and Paul Marshall have all been passed fit, with the latter named among the replacements.
Forwards Stephen Ferris, Dan Tuohy and Rory Best are back in the starting line-up after being rested for the Leinster game.
Ferris is a direct replacement for Henry in the back row, so Willie Faloon retains his place at openside flanker.
Nigel Brady drops to the bench for the return of Best, while Lewis Stevenson makes way for Tuohy in the second row. After impressing last Friday in his first game in five months, Declan Fitzpatrick will start again at tighthead prop.
Brian McLaughlin has named an unchanged back-line for Saturday's crucial game, meaning that Paddy Jackson gets the nod over Ian Humphreys at out-half.
The Ireland Under-20 captain produced an accomplished display at inside centre against Connacht two weeks ago, before controlling affairs in the number 10 jersey in the home defeat to Leinster.
This is Ulster's biggest game since they defeated Colomiers 21-6 in the 1999 European Cup final. McLaughlin admits some of his players are disappointed at missing out on selection for such an important fixture.
"Nobody wants to miss an occasion like this. These kind of games don't come around too often; it's been 13 years since we've had a game this big. It really wasn't easy selecting the squad this week," he said.
Commenting on the loss of Henry, McLaughlin stated: "It's a huge blow for us. He has probably been our most consistent player this season, probably over the past few seasons.
"I suppose we are fortunate in a way to have a player like Willie (Faloon) to come in. He is vastly experienced and will put everything into his performance on Saturday."
A big performance will be needed at the Aviva Stadium as Edinburgh will arrive full of confidence after an excellent Heineken Cup run.
"Edinburgh are one of the form teams in Europe. They beat Toulouse, one of the kingpins of the competition, and you have to respect them for that.
"They have a great spine, their pack is full of internationals and they have an excellent back row. They have international half backs who are very good at controlling the game so it will be a big challenge for us. They are not going to fear coming to the Aviva."
McLaughlin is confident that young out-half Jackson will rise to the occasion as well, adding: "Paddy has come in over the last few weeks and done exceptionally well. His performances have warranted selection.
"It's a very tough call on Ian (Humphreys) who has been exceptional for us over the past couple of seasons, but we felt Paddy deserved a shot."
The youngest member of the Ulster squad, Jackson had just turned 7 years of age when Ulster last played in a Heineken Cup semi-final against Stade Francais in January 1999.
Jackson said: "I was living in England at the time, we'd moved over there because of my dad's work, and I was more interested in football.
"I'm probably the one person in Ulster that doesn't really remember what they were doing in 1999!"
He is relaxed and confident ahead of this weekend's game in Dublin, admitting: "I'm delighted to be starting - I may be the youngest player in the squad but I have a job to do at 10 and I'm very comfortable making the calls.
"I'm playing right alongside Ruan Pienaar, with Paddy (Wallace) and Darren (Cave) outside me and Stefan (Terblanche) behind, so there's lots of experience around me.
"I find that it's best if I just try to relax before a game, I don't have a particular routine or hype myself up too much. I've talked to Neil Doak a fair bit this week and we've discussed how Saturday's match is just another game.
"Obviously there will be a massive crowd and a lot of media attention but it is just a game of rugby and I'll prepare for it in exactly the same way as I always do."
He added: "Doaky and Ian (Humphreys) have been a huge help to me as I've begun my professional career, providing tips and advice.
"When Brian announced that I was starting, Ian was the first person to congratulate me and told me to ask him anything I wanted. Obviously he knows the calls and plays just as well as I do, so it's great to be able to have that sort of support."
Tickets for the semi-final tussle are still available over the counter at Ravenhill. Alternatively, you can book online at www.ticketmaster.ie/erc.
ULSTER (v Edinburgh): Stefan Terblanche; Andrew Trimble, Darren Cave, Paddy Wallace, Craig Gilroy; Paddy Jackson, Ruan Pienaar; Tom Court, Rory Best, Declan Fitzpatrick, Johann Muller (capt), Dan Tuohy, Stephen Ferris, Willie Faloon, Pedrie Wannenburg.
Replacements: Nigel Brady, Paddy McAllister, Adam Macklin, Lewis Stevenson, Robbie Diack, Paul Marshall, Ian Humphreys, Adam D'Arcy.