The same question has been confirmed as a bug and was answered in this Octave Bug tracker post, which redirects to this forum post. Quoting the answer given by JasonNicholson as-is:
The key is that the environment variable "bell-style" must be set to "none" for MSYS which comes with Octave. There is two other options "audible" and "visible". Note that the "visible" setting seems to produce the same result as "audible" with Octiave 3.6.4 compiled with visual studio and msys/bin/sh.exe version 3.1.17(1)-release (i686-pc-msys).
1- You need to edit Octave-3.6.4\share\octave\3.6.4\m\startup\inputrc
2- Add this to the end of inputrc:
## Disable the beep!
set bell-style none
3- Restart Octave and check that it is disabled.
I know in coming years some will find this thread and the procedure will be a little different. I bet the key will be finding the "inputrc" file.