If you have InDesign CC 2019, when you select a Hyperlink and look in the Properties panel, you will see 3 buttons – ‘Remove Hyperlink’, ‘Edit Hyperlink’ and ‘Manage Hyperlink’.
Remove Hyperlink does what it says – it removes the hyperlink. However, it retains the applied Character Style which can be manually changed by clicking the [None] style in the panel.
Manage Hyperlink opens the Hyperlinks panel (if it’s closed) and Edit Hyperlink lets you edit it.
Hope this helps.
Adobe InDesign teamJaakko Juhani Pöntinen commented
It baffles the mind. I've an object to which I accidentally applied a hyperlink. I've yet to find a way to remove the hyperlink. There is no "Delete hyperlink" option anywhere to be seen.
Some guides say Right click -> Hyperlinks -> Edit hyperlink -> Delete, but I say: nope. No such option.
What if, creating an interactive-only .pdf, you'd have an object with a complex text wrap applied to it plus positioning plus other things and you accidentally hyperlink it. Delete the whole thing and start over? Yes. Maybe you don't have a save with the hard work done and no hyperlink mistake made. Maybe you've edited for quite a bit after the mistake and the undo levels just won't do. What then?
I cannot believe this oversight. But, yeah, us humans make mistakes :) That's for sure. Adobe employees and all.