There are many options (2021 update)…
Use a command line flag
pip <command> --disable-pip-version-check [options]
Configure pip from the command line
pip config set global.disable-pip-version-check true
Set an environment variable
export PIP_DISABLE_PIP_VERSION_CHECK=1
Use a config file
Create a pip configuration file and set disable-pip-version-check to true
[global]
disable-pip-version-check = True
On many linux the default location for the pip configuration file is $HOME/.config/pip/pip.conf. Locations for Windows, macOS, and virtualenvs are too various to detail here. Refer to the docs:
https://pip.pypa.io/en/stable/user_guide/#config-file