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.