I also had this error message, even though I was not connecting to an Access database, but to excel files in the Azure blob. The solution was to work only with xlsx or csv files, not xls files.
My access database is 32-bit but I have installed a 64-bit Power BI version.
When I try to install the AccessDatabaseEngine_X64.exe from https://www.microsoft.com/en-us/download/details.aspx?id=13255
I got an error that said I shoul uninstall all 32bit office software !...
You can install by command line:
After that Power BI 64bit can open Access databases.
I am new to Power BI. I too faced the same issue today. The versions of Power BI and Excel installed on my system are both 64 bits.
Did download the exe files (AccessDatabaseEngine.exe & AccessDatabaseEngine_V64.exe) as per resolution in the community, but the package installation failed and the installation was rolled back:
Importing access files from Excel one by one does work, but I do not want to follow the manual approach.