I was facing the similar issue. My env details - Python 2.7.11 pip 9.0.1 CentOS release 5.11 (Final)

Error on python interpreter -

>>> import mysql.connector
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ImportError: No module named mysql.connector
>>>

Use pip to search the available module -

 $ pip search mysql-connector | grep --color mysql-connector-python



mysql-connector-python-rf (2.2.2)        - MySQL driver written in Python
mysql-connector-python (2.0.4)           - MySQL driver written in Python

Install the mysql-connector-python-rf -

$ pip install mysql-connector-python-rf

Verify

$ python
Python 2.7.11 (default, Apr 26 2016, 13:18:56)
[GCC 4.1.2 20080704 (Red Hat 4.1.2-54)] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> import mysql.connector
>>>

The solution is to install corresponding Python 3 module:

sudo apt-get install python3-mysql.connector

It fixes import mysql.connector error:

$ python3
Python 3.5.2 (default, Nov 23 2017, 16:37:01) 
[GCC 5.4.0 20160609] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import mysql.connector
>>> 

And similar for Python 2:

sudo apt-get install python-mysql.connector

$ python2
Python 2.7.12 (default, Dec  4 2017, 14:50:18) 
[GCC 5.4.0 20160609] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> import mysql.connector
>>> 

You might want to check out the following article:

Can not get mysql-connector-python to install in virtualenv (Stackoverflow)

The accepted answer states the following:

Several things. There is an inconsistency in package naming so you may want to do:

pip search mysql-connector

to find out what it is called on your platform. I got two results mysql-connector-python and mysql-connector-repackaged.

so try this first:

pip install mysql-connector-python  

this may additionally give an error like this:

Some externally hosted files were ignored (use 
  --allow-external mysql-connector-python to allow).  

so finally this should do the job:

pip install mysql-connector-python --allow-external mysql-connector-python

It could be the case where you are running the Python file with the wrong Python installation. In VS Code we can choose the interpreter using which we want to run our Python file.

By default, the Python extension looks for and uses the first Python interpreter it finds in the system path. To select a specific environment, use the Python: Select Interpreter command from the Command Palette (Ctrl+Shift+P).

Just choose Python 3.8.9 from the list of interpreters. For complete guide you can refer to the documentation: https://code.visualstudio.com/docs/python/environments#_select-and-activate-an-environment