Is there any way, that I can make Android Emulator run on Azure Virtual Machine?

Something that requires virtualization isn't going to run in an Azure VM (which is already virtualized). Same thing with, say, WP8 emulator (see this question, with the same answer).

EDIT - As of mid-2017, there are now VMs that support nested virtualization (Dv3 and Ev3 series, for now). See this post for more information.