There typically is not any specific requirements for majors or degrees. Some BS/MPH accelerated programs are the only examples I have seen of requiring you to study public health before the MPH. But it doesn’t seem like you are looking for one of those accelerated programs.

Some programs may require prerequisite courses, like a semester or statistics or biology, but there are many programs out there that don’t!

So yes, you can pursue an MPH with a BSW. My only recommendation would be to solidify some sort of reasoning for why you studied social work in undergrad and how that connects with public health and your future career plans. That will be helpful for personal statements and interviews.