You are missing zlib.h header file, on Linux install it via:
sudo apt-get install libz-dev
As a matter of fact, the module presents as zlib1g-dev in the apt repo, so this is the up-to-date call (Feb 2019):
sudo apt install zlib1g-dev
On Fedora: sudo dnf install zlib-devel (in older versions: sudo dnf install libz-devel).
This will provide the development support files for a library implementing the deflate compression method found in gzip and PKZIP.
If you’ve already zlib library, make sure you’re compiling your code sources with -lz. See: How to fix undefined references to inflate/deflate functions?.