I am pretty sure it used to be possible to invite people who didn't have a Facebook account to a Facebook event, by email. However, I can no longer find a way to do this; the "Invite" link on a Facebook event page only seems to allow you to invite from your existing friend list?
Is it possible to invite non-Facebookers?
Best Answer
Yes, but not directly from Facebook and without the RSVP-on-Facebook Function.
There are three possible workarounds:
On the event-detail-page, on the right side under the cover, press the menu-button (···) next to the invite-button. Choose "Export Event" and you will download an ics-file (this is an iCalender-file). Then you could write your non-Facebooker an Email and attach the ics-file. The recipient's mail-client will recognize the ics and will offer to add the attached event into the personal calendar of the recipient.
You could invite anybody via Email also from your calendar, so you could have your personal RSVP-group. For that you export the event like described in the first possibility into your calendar and then invite anybody through your calendar's invite-option.
You go to the upcoming-events-page and look on the right sidebar for the last box which starts with "You can add your events to Microsoft Outlook, Google Calendar or Apple Calendar". There is a link "Upcoming Events" that you can subscribe into your calendar again, with all your upcoming events (so you'll have all Facebook-Events inside your Calendar). Then you can invite again as usual via calendar/mail. This last "list-subscription" is useful if you invite people to FB-Events via mail often and don't want to always export every event separately.