A recent update to Nightly (Firefox 44) has added ‘Do Not Disturb‘ option to ‘Content’ section in Options. If you enable it, no notification will be shown from the websites (to which you’ve granted the permission) until the restart of the Firefox browser.
Enabling Do not disturb for notifications in Firefox
Click on Firefox menu > Options > Content > Notifications, check ‘Do not disturb me‘, you can also add exception for the sites for which you want to show notifications.
You can manage notification permissions given to websites by visiting about:permissions page, we’ll cover more information about that in another post.