This link shows that the functionality did not exist in version 4.0.
VMs and Templates - Unable to move VM into Folder "The operation is not supported on the object."
Can someone tell me if this has changed in any subsequent release since, or is it still prohibited?
I think functionality remains same.
You can't move individual VM's which are part of vApp in to Folders, however if you want to achieve this then take VM out of vApp and then move(already mentioned in the link)