As a programmer finishing an MBA you will need to switch jobs to gain MBA related experience. Your VP should know this. While some jobs require splitting time between management and technical skills, those roles don't always naturally exist and sometimes need to be created. This means the issue is whether your new job will be with the same company or not.
Set up a meeting with your VP to remind him/her that you are about to complete your MBA. Assure the VP that you are interested in staying with the company. Ask what the VP sees as possible during the meeting. Maybe offer suggestions. Active engagement from the VP is required if you want to both stay with the company and use your new skills.
If you are met with resistance or no action is taken after some time has passed (even a follow-up call or note to assure you that steps are being taken), then you should plan to find a job with another company if you want to use your new skills. It might be a long time, if ever, before a role is found or created for you. Your "new" MBA could become a relic on the wall instead of a career change after a few years.
Based on your comment that the direct boss is pure software and your VP is "business", this is still valid although you may want to talk to your boss first. Inferences aside, the fact remains that you are getting an MBA and likely will be overqualified for your current job. Their best moves are either to do nothing or advance you. If this threatens your boss, then it is not a new threat. The news here is that you are about to complete your goal, while before you may have failed.
A conversation with your boss about what this means to your boss is polite. Mention that you want to put your skills to use and intend to talk to the VP about opportunities. Assure your boss of your dedication to the team and project and ask if there are options within the team.
Your only other option is to look for another job without these conversations, but to most managers that would be just as obvious due to the lack of communication and questions about internal opportunities.