The 20-year-old Egyptian complained of feeling unwell on the flight to Russia and the squad were re-routed to Berlin to enable him to receive medical attention.
An ambulance drove onto the airport apron and Elneny was assessed by another doctor before the flight resumed - after a 50-minute break - with the player declared fit enough to continue the journey.
"We had to stop the flight because Elneny was a little bit sick," FC Basel's head of media Josef Zindel told Press Association Sport.
"We had to make the stop because we weren't sure so we said it was better to go down and avoid making a mistake which you can't later make better.
"It was a question of safety and being sure and we had to decide quickly because, where we were in the air, Berlin was the last big city with major hospitals where we could go.
"The doctor and pilot said it was better to go down and then another doctor came and both said he was okay.
"He (Elneny) had not enough fluid and low blood sugar but he is okay now and he will train and he can play tomorrow [Thursday]."
Basel face Zenit in the Petrovsky Stadium in St Petersburg Thursday holding a 2-0 lead from the first leg.