I haven't looked, but I think you're going to have to do that manually.
Meaning, your application will have to check for the existence of the MySql installation the first time the user runs it. If it's not installed on the system, you will need to install it silently while displaying information about the database installation and progress to the end user.
Here's a link explaining how to install MySql silently.
When MySql is installed, you will need to create the database and populate it's tables pragmatically.
If there's a better way to do this, I'm not aware of it.
-Pete