Hi Tuymurod,
It would not be an issue for you to change jobs, and if the new job provides new challenges and opportunities for you to exhibit more leadership skills, it could help your application. Regarding your question about recommendations, it wouldn't be an issue to get a recommendation from your new manager as long as s/he can speak to your abilities and you have enough accomplishments by then for them to support their assessments.
As for your current manager, why wouldn't your current minister give you a recommendation if you apply next year? It's fairly common for applicants to submit LOR's from current and former managers. If the issue is that s/he would be upset with your move to another job, then that's a different story. Perhaps you can talk to him/her about your long term goals and how the move to Ministry of Foreign Affairs would help you get into your desired MBA program, which would be a step in you achieving your goals.
Best,
Cindy