Mechanical Engineering is a degree of very technical nature. Most of the people who have been in the field work for some time decide to pursue their MBA degree so that they can get a position at the managerial levels in relevance to mechanical engineering.
You can do a number of specializations in the field of MBA such as finance, marketing, Human resource, Information technology etc. You just need to understand that there are many marketing jobs in technical concerns that require an MBA + Mechanical engineering degree. Same is the case with finance and Human resource. So there is scope for all depending on your interest. However, I will recommend an MBA with a specialization in project management or marketing, because I believe they are a lot more in demand these days.