Hi Carlo,
As someone who decided to get a PMP certification several years after completing my MBA - my answer to your question is "Yes".
The reason is that the objectives of the two are drastically different.
A person can go through MBA learning all the core concepts academically of what it takes to run a successful business.
I got into Consulting after my MBA and I could make business plans, project financials and help organizations take strategic calls on which segments to enter into, based on the strength of my MBA degree. Some of my peers got into banking, either into quant intensive roles like risk modeling or into structuring complex products. Several other peers got into Marketing, which involves well, Marketing products and services

You get the gist..
But what an MBA teaches you is vastly different from what PMP teaches you. PMP ensures you are a "doer" not just a planner. It is a combination of the hard skills of organizing, coupled with the soft skills of constant negotiation with multiple stakeholders. PMP (and PM in practice) involves managing lots of real-life sticky situations, rather than only dealing with pure numbers or business plans.
This is not to say one is better than the other - just to say that you likely would come out of each of these with completely different skill sets.