Hellen,
Yes! You should download and install the 2007 Office System Driver: Data Connectivity Components. ArcGIS must need this specific version of the driver to be able to read xlsx files. Having a more recent version like Office 2013 would seem like it would have all of the previous drivers/components, but it doesn't. Click on the link shown above to get to the right driver.
I hope this helps!
Best Regards,
Tom