To mount .ko file using modprobe, one must have linux kernel headers:
Wrong Way to Install
Do not try to install, linux-headers-generic. It will gives the wrong kernel version.
Right Way to Install
> sudo apt install raspberrypi-kernel-headers
> uname -a and > sudo apt-cache policy 
to check the version of the kernel.
To find the corresponding kernel version of each raspberrypi-kernel-headers package, we can cross check with the github Makefile details, for example it is 4.4.38 in the link:
After headers are installed, they should be reflected as below:
Afterwards, install the kernel module (v4l2loopback) by simply:
> sudo apt-get install v4l2loopback-dkms
If successful, the following should be shown:
Finally, modprobe as usual and it should work now.