If you are using a standalone Ecommerce store, you can disable event contact notifications.  A standalone Ecommerce store is one found in the Commerce menu under Ecommerce.

To disable notifications in a standalone Ecommerce store:
1.  Go to Commerce > Ecommerce.
2.  Click on the name of the store you want to work with.
3.  Enter the Website Info page by clicking "Manage Website Info".
4.  Edit confirmation preferences by clicking "Ecommerce Form Options".
5.  Click on the Confirmation Text tab.
6.  Check to enable or Uncheck to disable the box labeled "Send me email notification for new purchases".
7.  Click the Save button.

This will allow listed email to receive or no longer receive notifications of purchases.  The purchaser still receives their confirmation.

It is not possible to disable just the Ecommerce notification when the Ecommerce store is part of a Kintera Thon event.
Ecommerce purchase confirmations are always sent to the purchaser.  You cannot disable these.