Try either
sudo apt-get install php-zip orsudo apt-get install php5.6-zip
Then, you might have to restart your web server.
sudo service apache2 restart orsudo service nginx restart
If you are installing on centos or fedora OS then use yum in place of apt-get. example:-
sudo yum install php-zip or
sudo yum install php5.6-zip and
sudo service httpd restart
