Last month, Instagram started testing its Archive feature that let you hide your photos. The feature is now rolling out to all accounts and should be available to everyone soon without having to update the app.
With Archive, you don't necessarily have to delete photos that you don't want others to see. Simply hit the Options button in the top right corner of your photo and hit the Archive button and it will be removed from your timeline but still available in your private folder. From there, you can choose to unarchive it whenever you want and it will be sent back to the same location in your timeline where it used to be.
The Archive folder will be accessible from a little rewind icon in the top right corner of your profile once the feature is available.