Elneny departed at the end of the first half, and Wenger said Arsenal are now awaiting confirmation of the severity of the injury.
"He has an X-ray, but I don't know how bad it is. But it doesn't look too good," he said, per Mattias Karen at ESPN FC.
The Egyptian was clearly in distress as he left the field, as shown by sports journalist Mootaz Chehade:
Early reports from Arsenal's medical staff suggested the injury was not too much of a problem. Freelance injury data analyst Ben Dinnery showed their initial prognosis:
However, Wenger's comments suggest the injury is serious, which could rule Elneny out of the rest of the season and potentially affect his involvement in the FIFA 2018 World Cup.
The Gunners have just four Premier League games to play but remain in contention in the UEFA Europa League. They play the first leg of their semi-final against Atletico Madrid on Thursday at the Emirates.
Bleacher Report's Sam Tighe noted how Elneny has been in good form recently:
Elneny notched two assists in Arsenal's quarter-final second leg draw with CSKA Moscow, but it would be a surprise now if he was fit for Thursday's clash.
His injury will be a blow to Arsenal with the club's hopes of securing UEFA Champions League football for next season now resting on winning the Europa League.
Egypt will also be monitoring developments closely as Elneny is a key member of the team. Hector Cuper's side have been drawn in Group A and will face Russia, Saudi Arabia and Uruguay.
James Benge at the Evening Standard said Elneny missing the World Cup would overshadow Wenger's Arsenal farewell:
Injuries this close to a major tournament always provoke major anxiety for players and national team managers. There will be real concern over Elneny who was clearly upset as he left the pitch and looked in some discomfort.