This is in no way related to malware of any kind.
Since the message didn't show up in your sent box, it's possible that it was sent from some other machine and your address was "spoofed" on the To line. It's also possible that your e-mail account has been hacked and the hacker deleted the messages he/she sent from your Sent mailbox. Changing your password will only help with the latter, but is a good idea regardless.
For more information, see: