How can I dismiss the App Store banner in Notification Center without taking an action?

Solution 1:

To dismiss the notification temporarily:

Click and hold the banner and flick it to the right to put that notification in Notification Center. If you are using a Trackpad, You can hover over the alert and use two fingers to flick it to the left.

The notification will still remain in the Notification Center until you update.

Unfortunately, there is currently no way to dismiss the notification permanently.

Solution 2:

Yep, duci9y's answer is the only real way to "dismiss" it. Unfortunately, Apple does not allow you to alter the type of notification. Therefore, there is never a close button. Now, if you are using a non-apple mouse, then you will have some problems doing duci9y's answer. I believe the only way you can dismiss it with a regular mouse would be to click on the notification button on the top right of the screen and then turn off notifications and then turn it back on.

It's not convenient, but that's how it works.