Steve Estes, Recent full-time MBA alum
As with most other top MBA programs, they don't require it, per se, but 99% of the people admitted have at least 2 years of full-time professional work experience.
Why? The primary metric schools are measured on is the impact they have on their students' careers and salaries. If you come to an MBA program straight from undergrad, employers are going to view you as "Analyst-level" and hire/compensate you accordingly. You may end up with a job at a great company, but you'll be at the bottom rung, not the 2nd rung. However, if you have a few years in the field and then get an MBA, you'll be recruited at "Associate-level", often with dramatically better salary and skipping to a level that would normally take several years for Analysts to reach. In industries besides Finance and Consulting, the same still applies but the titles may differ. So MBA programs realize they won't have the same level of career impact if they take people with no work experience - even if they'd get "first-round draft picks" by doing so. (not to mention that a lot of those first-round draft picks are choosing to go get paid very well by top employers)
The extremely rare exceptions are people who have incredible professional success already when applying, despite not having worked for a couple of years post-college. One example would be a guy I met who started and sold his own tech startup while in college (!) If you're in that category, you don't have to ask yourself if you are - you just know. And, likely, you wouldn't consider spending 2 years and $150k on an MBA to be the best use of your time and money. So, necessarily, those cases are rare.