Lately, I was trying to upload excel to my SharePoint 2013 site by using the Import Spreadsheet option, I got the below error

“The specified file is not a valid spreadsheet or contains no data to import”. File format and data everything was correct.

Workaround for on-Prem:
1. Open IE browser, then navigate to Internet Options -> Security Tab. And then in the “Select a zone to view… “, click Trusted Sites. Then add the site to the trusted site list.
Then Set the Security level for this zone of the Trusted sites to Low.
Now close the browser and open again.

Workaround for O365:
2. I got this solution from this technet URL. I have not tried
In Internet Explorer click Tools -> Internet Options.
Then Click Security -> click sites -> and add this URLs https://* and https://*

3. If you are running into issues on IE8, Try IE9, It worked for me

Hope one of the above workaround will work for you