MySQL Connector/ODBC requires Microsoft Visual C++ 2010 redistributable so you have to install it first.
If you want to install MySQL Connector/ODBC 32-bit version, you have to download and install Microsoft Visual C++ 2010 Redistributable Package (x86).
If you want to install MySQL Connector/ODBC 64-bit version, you have to download and install Microsoft Visual C++ 2010 Redistributable Package (x64).
After you installed Microsoft Visual C++ 2010 redistributable, you can try reinstall MySQL Connector/ODBC again, the issue should be resolved this time.
For me, I am installing mysql-connector-odbc-5.3.6-win32.msi, Microsoft Visual C++ 2010 Redistributable Package (x86) doesn’t work for me. However Visual C++ Redistributable Packages for Visual Studio 2013 works.
You can find Visual C++ Redistributable Packages for Visual Studio 2013 at
https://www.microsoft.com/en-us/download/details.aspx?id=40784