Cuper has admitted the loss of Elneny is a blow although he is hopeful the 24-year-old will be able to recover in time for the final, should Egypt battle their way past Burkina Faso.
They will face either Ghana or Cameroon who clash in the other semi-final game on Thursday.
Egypt is back in the African Cup of Nations final on its return to the tournament following a seven-year absence after winning a penalty shootout against Burkina Faso on Wednesday.
Tonight's match official is Malang Diedhiou (Senegal).
Apart from a handful of Egyptian supporters who have made their way here, the Pharaohs don't seem to enjoy much backing from the local fans.
In the penalty shoot-out, the Burkinabe goalkeeper Kouakou Koffi saved the very first spot kick from Abdallah El Said, but then Koffi was thwarted by opposite number Essam El-Hadary.
Egypt is undoubtedly the best footballing nation in Africa.
The Stallions got off to an encouraging start with Nakoulma forcing El Hadardy into a fine save, while Aristade Bance went close with a strike from distance in the 16th minute.
Egypt survived a barrage of attacks in the dying minutes, with Hadary the rescuer on several occasions, as the match went into extra time where both sides looked jaded, struggling to string passes together. "I don't know why they target players". Mohamed Salah with an outrageous finish into the top corner from the edge of the box from Elmohamady's set.
PENALTY SAVE! Burkina Faso 0-0 Egypt: El Said first up for Egypt and Koffi saves it onto the post!
Running the show for Egypt until this point has been AS Roma dribbler Mohammed Salah and Zamalek midfielder Mohamoud Hassan.
While they may not be blowing teams away, Cuper's men have needed to score just three times in four games thanks to a defence that is still yet to concede a single goal in Gabon.