Formal education? Potentially none, if you are good at teaching yourself, networking and learning from others.
The best way to get started in mobile app development is to get started in mobile app development. Many of the tools are free and there are lots of tutorials online. Pick a platform and go for it,
As others have mentioned, there are some other disciplines you'll need to study as well, particularly application security.
You will have to gain a background in computer science, and that means learning (among other things) how to code. Here are five areas you can research that could be potentially vital to your future with mobile app developing:
- Cross-Platform Development (UX/UI design)
- Cloud Computing
- Internet of Things
These are good places to start with. Good luck!
Good luck to you!