Created into WordPress is a feature that allows a blog owner to be informed through e-mail each and every time a new comment has been posted.

Step 1: First of all go to Setting > Discussion.

Then scroll down this page and you can see two Checkbox options:

1. Anyone posts a comment

2. A comment is held for moderation.

Step 2: Disable these 2 options and save them.

The comment notification emails are enabled by default on all posts or pages.