<p>I am looking to protect the code of my Firefox extension because it has server calls in it that no would be a security risk if someone could make them outside of the extension. Any suggestions on how to encrypt it?</p>

If it's going to be executed on the client side, with no reliable secret, then basically you've definitely got a security vulnerability.
It's hard to suggest ways round this without knowing a bit more about your extension. An obvious suggestion would be to request a username/password, authenticate (over HTTPS) with the server and receive a time-limited token, and then present that token with the "dodgy" request. That won't stop anyone with the right username and password though...