May I ask why you want to leave?
I work in corporate finance so here’s my understanding. You do not need an MBA to switch but you will need something to get your foot in the door. You would need to have some other work experience in a related field, get an MBA at a top 25 school and use their recruiting resources to land a gig, know somebody within the company who has enough clout to get you a job.
I think it would be easier to try and get into less prestigious company doing consulting first, your DMD might show them you’re intelligent enough, then work a few years doing that while moving over and then move to McKinsey.