If your MySQL server accepts remote connections and you have a static public ip you can simply replace localhost (127.0.0.1) by your public ip in the connection string. If you don't have a static public ip you can use a Dinamic DNS service (e.g. noip.com) to point towards your sql server.
Another option, if you dont need to update the data frequently is to export your data to a file and deploy it along with your app instead of making an odbc connection.