Enable email notification and exclude that same alert to appear in active alert dashboard.

All alerts have the default "Message to display when the alert is triggered" field in the Alert Actions. If all you want to do is keep it from displaying in alerts widgets when it fires, you can clear that text box.

However, if the intent is for this alert not to be visible or display for certain people or groups, I would recommend using an Alert Limitation. It's cleaner and it also preserves the details of displaying and visibility for the alert, for users who need to see it. 

https://documentation.solarwinds.com/en/success_center/orionplatform/content/core-setting-trigger-actions-and-escalation-levels-sw1031.htm 

https://documentation.solarwinds.com/en/success_center/orionplatform/content/core-setting-alert-properties-sw1019.htm 

Removing the alert message does not result in removing the alert from the 'Active Alerts' list.  Doing so would just cause the message field to be empty. 

Alert Limitations would be a viable option, granted you want to have an account alert limitation applied to all accounts and then the alert in question. 

sorry, meant that it doesn't display details ;) Account Limitation would work as well, if you want to have the limitation apply system wide, and not just on the alert itself. There are use cases for both. Depends on what the goal is. 

sorry, meant that it doesn't display details ;) Account Limitation would work as well, if you want to have the limitation apply system wide, and not just on the alert itself. There are use cases for both. Depends on what the goal is.