The short answer to your question is: No, the MySQL database cannot be "embedded" in a jar file.
If you have built your application to require a connection to a MySQL database, then you will need a MySQL database server running somewhere. (The MySQL server doesn't have to be local to the box; you can connect to a remote MySQL server, although that adds a dependency, so may not be the way you want to go for a "standalone" application.
If you need an "embedded" database for a "standalone" application, you might want to check out some different databases, e.g.
Java H2 database engine: http://www.h2database.com/html/main.html
Apache Derby: http://db.apache.org/derby/
MySQL has stopped development and support for MySQL Connector/MJX http://dev.mysql.com/doc/connector-mxj/en/connector-mxj.html which wasn't a truly embedded database; it was really a mechanism to automatically start a MySQL instance and initialize a database when a JDBC connection was requested.