Off the top of my head: the VM executes either HLT or MWAIT, and those instructions are generally programmed to cause a VM exit, so the hypervisor can take action. The hypervisor will deschedule the VM and possibly go idle itself.

TBH, I have no idea how MONITOR works in a VM. It might be quite messy.

Edit: Here's a really nice explanation: http://www.contrib.andrew.cmu.edu/~somlo/OSXKVM/mwait.html