I would write a script (PHP, Python, etc.) to upload the spreadsheet to MySQL and set up a scheduled job (cron on *nix) to run that script. You should be able to connect to the spreadsheet from a scripting language with ODBC, just like your internal program.
Or you can write VBScript in a spreadsheet that connects to MySQL through ODBC and pushes the data to it. If you set the script to run automatically when the spreadsheet loads then you can schedule a job to load the spreadsheet.