If you only need zip and not a zip extension for a particular language (like PHP) this will do the trick:

apt-get update
apt-get install zip unzip

If you are running a PHP application and require the zip extension you can run:

apt-get update
apt-get install php7.0-zip 

it worked for me… thank you @ryanpq

adding a [solved] tag to make it easier for other to find this fix.

You may prefer using :

apt-get install zip unzip -qy

to have a quiet -q and more important -y to force Yes when being ask:

After this operation, 1,117 kB of additional disk space will be used.
Do you want to continue? [Y/n]