Using another Asterisk box to do this is possible, though not terribly simple.
Assuming that you just want to check that the IVR answers and starts into the menu, you need a tone or sound file that can be programmatically analyzed. You dial into the IVR using the other Asterisk box while recording the call, hang up after a few seconds, then perform analysis on the recorded file. If you find the waveform you expect, the system is up. If not, you can raise an alarm.
If you need to test deeper levels of the IVR, you can have multiple tones.
This may require some more advanced signal processing out there, but the techniques for doing such analysis is well documented. Simpler analysis will do if you're just trying to determine if you've received your tone instead of a PSTN announcement.
The tone tends to be something customer friendly, as it will be heard by people calling in as well (unless you use a different route into the IVR and use conditionals in the dialplan to decide whether the tone is played). Of course, at that point you're not really testing the IVR the customers use.