This issue has been closed as 'Won't Fix' due to an extended period of time without updates. If this issue is important to you please let us know by posting on the AnswerHub or UDN, and Epic will re-open the ticket for further review.
https://udn.unrealengine.com/questions/270801/cannot-open-modules-panel-its-missing.html
MikeF: The "Modules" button will automatically become hidden if the
editor thinks that the user is not a programmer. It checks to see if you
have C++ project files for your project. See the CanShowModulesTab()
function in ToolboxModule.cpp
There's no existing public thread on this issue, so head over to Questions & Answers just mention UE-24063 in the post.