Question about spousal visa

I am an american and I have been in Japan for about 2 years while in the military. I am engaged to an Indonesian that is here on a working visa. Is it possible for me to obtain a spousal visa to stay here in Japan after being discharged to go to school?

The spouse visa is for spouses of Japanese nationals. Once you get married to your fiance(e), you can apply for a dependent visa. On this visa you can apply for permission to work part time (up to 20 hours a week).

Hi, I do believe in order to get the spouse visa in Japan your wife needs to be Japanese OR you marry a naturalized Japanese citizen.

Your alien card ('gaijin card') status will then change to 'spouse of Japanese national' enabling you to do just about anything except own land in Japan.

Dunno about getting married in Japan to non-Japanese, but I think you'll be out of luck getting anything like a spouse visa.
Maybe contact the school you want to attend and ask to sponsor your visa eligibility as 'student'?

As Sira stated correctly, Ryan, you will be eligible for Dependent status, not Spouse (to a Japanese national, etc.). Under Dependent status, you will be able to live together with your wife in Japan, to study, and if you obtain a separate permit, to work part-time. The conditions aren't that much different from that of Student (university) or Pre-college student (language school) status, so you will be fine in terms of visa status for staying in Japan and attending a university/language school.