Generally, a B.A. is a minimum requirement for this gig. Some programs do exist for folks to earn a two-year degree in events management or public relations, but generally, the companies want their events planners to have the same amount of experience as all of their other employees (source).
Companies also really like to grow people on the inside, so if you can get that entry-level assistant position, you might end up getting set for life.
Beyond formal education, there are also professional organizations you could join such as the Convention Industry Council or the Event Planners Association. These will help bulk up your résumé while you're on the hunt for a job. They'll even invite you to networking events.
That's right—event planners planning events for event planners. This must be what ice cream makers feel like in Alaska.