Intro.

I was tried to modify a kvm kernel module for my research. Because it was a built-in kernel module, I needed to build all the kernel source code after modifying kvm module which is located in path arch/x86/kvm/ from the linux kernel source root.
The whole kernel compilation was a time consuming job, usually taking over 10 minutes even on my i7 desktop machine. I tried to find a way to compile modules only without the whole kernel compilation. The solution and some troublesomes are described below.

Assumptions

It is assumed that you have a kernel source code and configured it properly according to your taste. Also, assumed that you had installed the kernel and rebooted with it.

Solution

Building only one module is easy. After configuring, build the source as following.

make M=path/to/module/directory
make M=path/to/module/directory modules_install

You can find the path of modules with modinfo command.
In my case, the required module was kvm.ko, and kvm-intel.ko. They were located in arch/x86/kvm.

make M=arch/x86/kvm
make M=arch/x86/kvm modules_install

You can reload the new modules. I removed the kvm-intel module first because it depends on the kvm module.

sudo rmmod kvm-intel kvm

And, load the new modules.

sudo modprobe kvm
sudo modprobe kvm-intel

or just loading kvm-intel will load kvm automatically.

sudo modprobe kvm-intel

FYI, the new modules are installed in /lib/modules/`uname -r`/extra directory.

Troublesomes

1. modprobe failure.

modprobe: error: could not insert 'kvm': exec format error

The modprobe might fail if the version of a kernel module and that of a kernel are different. You can check the error with dmesg after the modprobe failure.
In my case, I built the kernel without any modification which resulted in the version number of 4.13.0-rc6. When I modified the kvm module and compiled it, the version number was changed to 4.13.0-rc6+. Linux kernel source code appends + to the version number as LOCALVERSION if any source code is modified. (It might be related to git’s uncommitted or unstaged changes. I did not confirmed yet.)

My solution was building the kernel with some small modifications generating the version number as 4.13.0-rc6+ as a baseline.
The problem solved because the kvm module was also built with the same version number, 4.13.0-rc6+, which did not produce any modprobe error.

2. Location of generated modules

The modules generated with M=path options are installed into /lib/modules/`uname -r`/extra path. The path is different from the originally built one (when compiling the whole kernel) which is /lib/modules/`uname -r`/kernel/arch/x86/kvm in the case of kvm.

If you want to install a new module into the same location of original one, use INSTALL_MOD_DIR option. Example follows.

sudo make INSTALL_MOD_DIR=kernel/arch/x86/kvm M=arch/x86/kvm modules_install

Note that you have to do sudo depmod -a before modprobe the new modules. Otherwise, modprobe will fail.