Access Chess.com through a browser.
Go to Home---->Account.
Then click on Alert & Email Settings [Manage your alert & email settings]:
http://www.chess.com/home/alerts
Scroll down to "Email Settings" and un-check the box for "Also send alerts to my .....".
Make sure you click the "Save Changes" button before leaving the page :)
Is there a way to turn off email Notification without turning off the move Notification. I am using android.