If you delete a Fiverr gig with reviews, the reviews will be gone as well.
If you don't want to promote or sell a gig for personal or technical reasons, go to your Fiverr seller dashboard and "Pause" it.
The gig will be removed from your active gig listing immediately. You will, however, always have access to the "paused" gig and will be able to restart it in the future.
Recommendation: I would not advise deleting a gig (regardless of your personal reasons). Sometimes a previous customer may return and want the same gig. They may seek a change to a previous engagement or a new service. Because this has happened to me multiple times, I would not advise you to delete your gig.
Hope it helps you.