Despite being sick before the game, Wenger said the midfielder insisted that he was fit to play against Southampton.
Elneny was taken off before half-time in their 2-0 home loss to Southampton in the quarter-finals of the English Football League (EFL) Cup.
Arsenal manager, however, revealed that it was the midfielder who insisted that he was fit to play.
"He was sick before the game. He decided he felt well enough," Wenger said.
"I could see after five or 10 minutes that he was not right. He has no medical injury problem, but he has diarrhea or a stomach problem."
Gunners were beaten at home by Southampton, their first loss since their opening day defeat to Liverpool.
Speaking on the loss, Wenger refused to give an excuse, admitting that Southampton were the better team.
"We had a disappointing performance, especially in the first half. We were not good enough defensively and we gave cheap goals away,” The French manager said.
"We were not incisive enough. They defended deep and were sharper and fitter than us. With a two-goal advantage, they defended very well."
Arsenal will next make a trip to the Olympic Stadium to face West Ham in the Premier League on Saturday, December 3.