I am referring the following tutorial to make a login page for my web application. http://code.tutsplus.com/tutorials/intro-to-flask-signing-in-and-out--net-29982
I
It depends on Python Version as well in my experience.
If you are using Python 3, @DazWorrall answer worked fine for me.
However, if you are using Python 2, you should
sudo pip install mysql-python
which would install 'MySQLdb' module without having to change the SQLAlchemy URI.