So I spent about 5 hours trying to figure out how to deal with this issue when trying to run
./manage.py makemigrations
With Ubuntu Server LTS 16.1, a full LAMP stack, Apache2 MySql 5.7 PHP 7 Python 3 and Django 1.10.2 I really struggled to find a good answer to this. In fact, I am still not satisfied, but the ONLY solution that worked for me is this...
sudo apt-get install build-essential python-dev libapache2-mod-wsgi-py3 libmysqlclient-dev
followed by (from inside the virtual environment)
pip install mysqlclient
I really dislike having to use dev installs when I am trying to set up a new web server, but unfortunately this configuration was the only mostly comfortable path I could take.