How do you temporarily disable your Instagram
There's currently no way to temporarily disable your Instagram account. When you attempt to do so, Instagram's website explains that a user can only permanently delete their account. This is stated in their Help Center as well.
Once you delete your account, all files and photos will no longer be recoverable and there's no way to reactivate your account. You can sign up again later, but will not be able to use the same username ever again.
Tip: One way you could achieve a similar result would be to simply remove all of your photos from Instagram and delete all of your comments. You could also make a picture using a graphics application that tells your friends and others on Instagram that you're taking a break from using the site.
Of interest, Instagram Direct is the newest way to privately send a video or photo to a select group of people. You don't have to worry about posts appearing in your profile, search, or feed. Before you can access the new feature you will need to download the 5.0 version of Instagram from the App Store or the Play Store.