Basically, yes. For an MBA, one needs a bachelor (B.A.) degree, as
Sharkalissa mentioned: MBA means "Masters of Business Administration",
a degree that follows the bachelor degree.
However, some MBA programmes do accept students without a bachelor
degree, based on life experience or other elements:
Edinburgh Business School (Distance learning): "If you do not have a
first degree, you may become a matriculated (i.e. enrolled) MBA
student by meeting the requirements for the award of a postgraduate
certificate. This requires you to pass examinations in three MBA
courses, one of which must be a core course." (SOURCE: Edinburgh
Business School MBA, Admission
James Cook University (Australia)
Entry into the MBA without a bachelor degree is dependent on
successful completion of Graduate Diploma of Management at a credit
University of Western Australia
If you do not have a first degree, it is still possible to use your
management experience as a basis for entry to the Graduate Certificate
or Executive MBA courses.
"If you do not have a university degree, but feel you have comparable
life and work experience, talk to our faculty. We will assess people
on an individual basis, although it is rare that anyone is admitted
without a degree."
Manchester Business school
"If you do not have a bachelor degree then you must be at least 27
years old. You will need to complete an additional essay ? details in
your application pack."
You may find other schools that have even moer lax admission policies
but be warned: I also found schools, such as "Mount Rushmore
University" (www.rushmore.edu) that offer admission without a B.A.
However, these schools are not accerdited institution, their degrees
are not recognised or reputable, and without refering to that specific
school I've mentioned, some of them are known to be "diploma mills".
Check the reputation of a school before you enroll.
At the end, let me recommend to you to consider making the necessary
courses that would turn your associate degree into a bachelor one.
There are many distance learning possibilities, but it might be easier
to check first with your local community college.
I hope this answered your question. Please contact me if you need any
clarifications on this answer before you rate it. My search strategy
included looking for [MBA + "without a first/bchelor degree"].