NO. MBA programs accept students in any undergraduate field. They prefer students who do not have a business major because they give you the business training but they cannot provide the broad background that managers should have. The best majors are in the sciences, engineering, or math, but other majors are also suitable. Religion? Religious organizations need good management. Theater arts? Entertainment businesses need good management. Tourism? Hospitality businesses need good management.
MBA programs prefer students with 2-3 years work experience after the first degree. Some accept students right out of college if they have good grades and a high GMAT score. Some MBA programs are designed specifically for new college graduates without work experience. But in those programs you don't get the benefit of learning from other students who have work experience. A lot of valuable learning takes place through class interaction. Also when you graduate your job offers will be about the same as a business undergraduate gets because you have no work experience, and you've been two years out of your undergraduate field so it's hard to get work in that area.
Explore the Official MBA Guide. It's a comprehensive free public service with more than 2,000 MBA programs listed worldwide. It allows you to search for programs by location (US, Europe, Far East, etc.), by concentration (finance, marketing, aviation management, health management, accounting, etc.), by type of program (full-time, distance learning, part-time, executive, and accelerated), and by listing your own criteria and preferences to get a list of universities that satisfy your needs. Schools report their accreditation status, tuition cost, number of students, class sizes, program length, and a lot of other data. Schools provide data on entrance requirements, program costs, program characteristics, joint degrees, and much more. You can use the Guide to contact schools of your choice, examine their data, visit their web site, and send them pre applications. You can see lists of top 40 schools ranked by starting salaries of graduates, GMAT scores, and other criteria.