A hypervisor runs multiple Operating Systems, having each one think that it has access to the whole of the hardware.
A microkernel is one way of writing the kernel of the Operating System, so that each part of it is a separate process, routing messages to each other in a safe manner to get things done, rather than doing direct calls to each others code.
With a hypervisor you wouldn't expect each of the OSes to have any communication with each other at all, whereas with a microkernel you'd expect the different processes to talk to each other a lot.
You can, apparently, repurpose a microkernel as a hypervisor, but I don't know anything about that at all. Presumably the infrastructure is quite similar.
There is a lot of controversy about the distinction between VMMs and microkernels. A view from the microkernel side is given in http://www.ertos.nicta.com.au/publications/papers/Heiser_UL_...