I found that when the object in the scene is focused, the timeline preview will be activated. So just click on other objects first, and then directly drag the playableDirector Object into Prefab.

Thanks to YoloJero, the simple solution of unchecking preview in the timeline window worked for me!

add playableDirector component to a prefab instance and override it will cause unity crash.

YOLOJERO's workaround seems to work.

Some clarification about why this is by design would be great. This is certainly causing conflicts in our workflow not being a prefab.

Here is the solution I just found:

In the "Timeline" Window deactivate the "Preview" => now you can save it as prefab :)

Not sure why this is by design as it works fine once after a restart. It's not like it's disabled by design unless you restart - that's surely a flaw not a design choice.
E.g. Create a timeline, parent stuff to it, try to create a prefab (won't work). Restart Editor, try again, works!

Also GTZPower, the disabled apply button seems to only be the root with the Playable Director on it. You can apply from the sub-objects just fine.

Sorry, should have read more closely: why is this by design?
In my case, the timeline is only referring to children of the object that I want to make a prefab, so everything is self-contained.
The OP's workaround doesn't work completely, as my control-track references to sub-timelines are invalidated when the prefab is instantiated.

Still an issue in 2018.1.3f1

Also seeing this issue in 2017.3.1f1. I am unable to apply changes to an existing prefab with a playable assigned to the Playable Director component. Clear the playable assignment, and the "Apply" button becomes enabled.