For all those using Ubuntu with ppa:ondrej/php
PPA this will fix the problem:
apt install php7.0-mbstring php7.0-zip php7.0-xml
(see https://launchpad.net/~ondrej/+archive/ubuntu/php)
Thanks @Alexandre Barbosa for pointing this out!
EDIT 20160423:
One-liner to fix this issue:
sudo add-apt-repository -y ppa:ondrej/php && sudo apt update && sudo apt install -y php7.0-mbstring php7.0-zip php7.0-xml
(this will add the ppa noted above and will also make sure you always have the latest php. We use Ondrej's PHP ppa for almost two years now and it's working like charm)