An MBA may do 4 positive things for you, especially if it is a prestigious one:
It will teach you various established frameworks and methodologies for dealing with business management issues, introducing topics like business strategy, managerial accounting and financial planning, applied micro- and macro-economics, and applied psychology and business organization. People will argue that you could learn all this on your own from books, but would you take the time? And there is value to someone having designed a standardized curriculum about it.
It will train you up in the "case method", i.e. exercises by group work where you are given background on a business problem and work through some very concrete and some very open-ended questions about it, and present orally and in writing in class about it. There's nothing magical about it, but it teaches you ways of structuring your time, communicating your results, and working in groups (including dealing with minor interpersonal friction) which all have important differences versus sciences and/or engineering.
You will network with your MBA peers, who will form a cohort of mutual support through upcoming decades of your career as you switch from technical to business/management. Many MBAs feel this is the most important of the benefits.
You gain a credential as well as create a breakpoint in your career. There is lots of recruiting on MBA campuses, so you will have lots of opportunities to explore career alternatives; much easier to access than if you were rising from technical to managerial ranks at your current employer only. Even if you return to your current employer, you now have a demonstrable credential and a jolt of external knowledge and validation that is quite likely to earn you at least some respect, and "mark" you as being suitable for a technical->business transition.
It will however:
- Cost oodles of money, likely putting you in debt for several years (unless your current employer pays for it), and carries the opportunity cost [that's an example of MBA-speak for you] of 1-2 years of your life you're not getting back.
As to salary, it depends. Pretty clearly the starting salary of an MBA > undergrad CS degree only. By and large, it will probably pay off long term (even after the debt + delay in point 5), but there are definitely niches in computer science where the right expertise is scarce and the sky is the limit for $, and arguably the lifestyle-adjusted $ is higher. But as to whether this will persist over the duration of a career is anyone's guess.
[My germane background: precocious young software developer decades ago, then math Ph.D., then several years in business/consulting/management in roles where my peers had MBAs but I didn't. Now freelance consultant and part-time academic/teacher, including in business schools.]