Apple - How to upgrade Homebrew itself (not softwares/formulas installed by it) on macOS 10.12.3?

To update homebrew itself, use:

brew update

To upgrade all packages installed using homebrew, then you have to use brew upgrade. You can check this FAQ from brew website for more details.

The right way to solve this is to enter:

$ cd "$(brew --repo)" && git fetch && git reset --hard origin/master && brew update

Found at http://discourse.brew.sh/t/how-to-upgrade-brew-stuck-on-0-9-9/33.