Also absent is Simon Danielli, who picked up a shoulder injury during last Sunday's Heineken Cup match against Biarritz.
The Scotland international joins Smith, Cave, David Pollock, Declan Fitzpatrick and Adam Macklin on Ulster's injury list.
But Robbie Diack is expected to make the trip to Murrayfield. He sustained a sternum injury when trying to score a first half try against Biarritz. The South African back rower played on until being replaced by Chris Henry in the 62nd minute.
Meanwhile, Mark McCrea, Jonny Shiels, Tommy Seymour, Nigel Brady, Ryan Caldwell and Willie Faloon all come back into contention, after lining in the Ulster Ravens' British & Irish Cup victory in Swansea.
The Ulster starting line-up and replacements to face Edinburgh will be announced on Thursday afternoon.
ULSTER Squad (v Edinburgh) - Backs (13): Adam D'Arcy, David McIlwaine, Tommy Seymour, Mark McCrea, Andrew Trimble, Jonny Shiels, Nevin Spence, Ian Whitten, Paddy Wallace, Ian Humphreys, Niall O'Connor, Paul Marshall, Ruan Pienaar.
Forwards (16): Tom Court, Paddy McAllister, Bryan Young, BJ Botha, Rory Best, Andi Kyriacou, Nigel Brady, Tim Barker, Dan Tuohy, Johann Muller, Ryan Caldwell, Willie Faloon, Robbie Diack, Stephen Ferris, Pedrie Wannenburg, Chris Henry.