Although Instagram automatically defaults all new accounts to public visibility, you can use your profile options to configure your profile as private. With this setting enabled, all photos you upload are only viewable by followers who have received your approval first. If you change your mind later, you can disable this restriction and make your profile public again in the main profile options.

Disabling Privacy Restrictions

With the Instagram app launched, navigate to your profile by tapping the "Profile" icon, which is located to the far right and looks like a contact card. Tap "Edit Your Profile" to display the profile options. Then scroll to and disable the setting for "Posts Are Private."

Limiting Specific Users From Visibility

Any Instagram user can view a public profile, but you can still restrict access to specific users by blocking them. Navigate to the user's profile and tap "Block User" to establish the restriction. This feature does not otherwise affect your account's public visibility, but it prohibits that user from accessing it -- and the user will not be notified of the block.