To hide the “Upload Multiple Files..” link and from the ribbon we should add the below mentioned script in my CSS file (custom CSS file used of my master page). This will hide for all documents libraries for which this CSS is applied.
#ctl00_PlaceHolderMain_UploadDocumentSection_ctl03_UploadMultipleLink, #Ribbon\.Documents\.New\.AddDocument\.Menu\.Upload\.UploadMultiple-Menu32
{
display: none;
}
#ctl00_PlaceHolderMain_UploadDocumentSection_ctl03_UploadMultipleLink, #Ribbon\.Documents\.New\.AddDocument\.Menu\.Upload\.UploadMultiple-Menu32
{
display: none;
}