What language are you using? PHP? The zip PHP extension is installed. What's a minimal test case that gives you the error? Is there any more to the error message? Creating a ZipArchive works fine for me.
Code:
$z = new ZipArchive();
You can also use the zlib extension to compress data.
What host are you on? The samples work on Lotus. Sometimes some extensions accidentally get left out when PHP is built. The best course is to open a support ticket.