What education is needed for a career in Media Production?

Well, there are universities which offer courses titled "Media Production".
But that's just a general answer to your query.
Allow me to elaborate.
Media production is a vast industry can be divided in to several industries such as television, film and video, and Internet media.
Several universities, colleges and other educational organizations offer courses which are tailored for the mentioned industries.
You will need to decide which field, in media production, you feel comfortable with or think have the talent for.
For example, "editing" is an important process and has several specialization courses.
It's a tedious, time consuming process which requires that the person editing pays attention to details.
I would recommend that you look in to Media Production as an industry and choose a field to work in, and then look in to courses which are being offered by educational organizations.
I would love to help you further.
Please let me know.