If [man]ZIP[/man] support is enabled (or any non-core PHP extension/library, for that matter), then as dagon suggests [man]phpinfo/man will have a table under the 'Configuration' section (and above the 'Environment' section) preceded by the name of that extension/library. If you don't see the table (note they're sorted in alphabetical order), then you probably don't have that extension/library installed or enabled.
Alternatively, you can use: [man]extension_loaded/man to check if a certain extension is loaded, [man]get_loaded_extensions/man to get an array of all loaded extensions, [man]class_exists/man to check if a certain class has been defined (e.g. ZipArchive), or even [man]function_exists/man to check if a certain function exists (e.g. [man]zip_open/man).