Qualifications
None.
The best part of being an entrepreneur is that if you can create a successful business, you're already qualified. Business principles like marketing and finance can be taught and learned, but the true entrepreneur understands that the proof is in the product.
A degree in just about anything proves you can stick to a task, but your ability to sell yourself and your ideas will be critical two times. First, when you present your idea to someone who wants to buy it, and second, when you want an investor or a bank to give you enough money to get your business up and running.
Of course, it helps if you have a story. A true story. Entrepreneurs are experts in solving problems. Mothers who design better baby products are a good example. A pilot with a new flight plan algorithm for on-board navigation software, a burn victim with a new recovery tool.
Each knows how to describe the problem, the possible consequences, and the rewards of fixing that problem. These people have the most important qualification of all: passion. Sometimes, the mere fact that you are risking everything for the product is proof of that passion, so be sure you're ready to tell your story over and over. And over.
But real qualifications, like a certificate? A degree (source)? You're the boss. What do you need to prove to yourself that you've got what it takes?