I specified the particular version of python it’s 3.7
And that helped me

I have installed these ones:

sudo apt-get install python3.7-dev libmysqlclient-dev

And then installed mysqlclient by:

pip install mysqlclient

I turned out, that the solution is slightly different for almost every Python version. For those using different versions, such as Python 2.x, 3.5 or 3.7 I found this:

Part I

For Python 2.x use:

  $ sudo apt-get install python-dev

For Python 2.7 use:

  $ sudo apt-get install libffi-dev

For Python 3.x use:

  $ sudo apt-get install python3-dev

For Python 3.4 use:

  $ sudo apt-get install python3.4-dev

For Python 3.7 use:

  $ sudo apt-get install python3.7-dev

For Python 3.8 use:

  $ sudo apt-get install python3.8-dev

For Python 3.9 use:

  $ sudo apt-get install python3.9-dev

Part II

If this still doesn’t help, others have pointed out to install

  $ sudo apt-get install build-essential

and finally

  $ sudo apt-get install libssl-dev

But the last two didn’t help myself – but hoping this might help you!

You may do this before:

sudo apt-get install python3-dev default-libmysqlclient-dev build-essential

Source: https://pypi.org/project/mysqlclient/

This issue was persistent in Ubuntu and python 3+. In my case, I was using Ubuntu 18.04 and found this solution to be useful for python version 3.7.5

Step 1. Install libpython3.7-dev via sudo apt

> sudo apt-get install libpython3.7-dev

Step 2: Install mysqlclient

> python3 -m pip install mysqlclient==1.4.6

I wanted to install the ‘Modoboa’ mail-server package (https://github.com/modoboa/modoboa) on my Ubuntu 18.04 with Apache as my webserver, instead of nginx. I needed mysqlclient for Python 2.7. The following packages worked for me:

sudo apt-get install libssl-dev gcc python2.7-dev libmysqlclient-dev

I’m using the python3.8. Similarly to david’s answer, use the following command then it works.

$ sudo apt-get install python3.8-dev