1. Download from official website installation package for the correct version for your system
2. Run the program on Linux Mint
Intel Linux Graphics Drivers Installer, when run, makes the test of name distribution, and if it's not Ubuntu, it refuses to work. Therefore we will make so that the program "thought" that running in Ubuntu.
Intel Linux Graphics Drivers Installer for Linux
In my example I run on Linux Mint 18 (this corresponds to Ubuntu 16.04)
Open in a text editor the file /etc/lsb-release
sudo xed /etc/lsb-release
Do the contents to the next view
#DISTRIB_ID=LinuxMint #DISTRIB_RELEASE=18 #DISTRIB_CODENAME=sarah #DISTRIB_DESCRIPTION="Linux Mint 18 Sarah" DISTRIB_ID=Ubuntu DISTRIB_RELEASE=16.04 DISTRIB_CODENAME=xenial DISTRIB_DESCRIPTION="Ubuntu 16.04 LTS"
Now nothing prevents you, run installer and update intel driver.
Don't forget the /etc/lsb-release file back to its original appearance.
3. Reboot the system