Diehl told WLS-TV she "wasn't at liberty" to discuss the pictures, which were later removed from her Facebook.
"The activity portrayed in the photo absolutely goes against Spirit policy," airline spokesman Paul Berry said. He said the company is investigating the photos.
Sylvester Pittman, a former flight attendant who now works as an aviation consultant, said it is not uncommon for crew members to take similar pictures.
"I have a picture in a jet engine, and pretty much everybody that I know that has been a flight attendant... it's just one of those things that we like to do," Pittman told ABC News.
Heather Poole, a flight attendant and author, also defended Diehl.
"The photo of the flight attendant in the engine isn't a problem. We all take them. The time that she decided to take it could be an issue," she tweeted.