Hi,
You need to have compressing softwares installed for this. E.g winzip, WinRar, 7- Zip etc. . Winzip and WinRar are licensed but 7-zip is an opensource.
You can create a Bat file that will call the zipping executable with correct arguments passed from the SSIS parameters and use the execute process task to call this bat file for compressing.
An example of how to achieve this using 7-Zipcan be found in the link below,
http://sqlage.blogspot.se/2013/12/ssis-how-to-compress-and-archive-file.html
You can use the for each loop container to compress individual files , or change the argument in the bat files to compress the entire folder.