Mono does not integrate into MySQL (that I know of), but it sounds like the version of libz that ships with Mono is being given priority over the one that ships with Linux (typically in /usr/lib or /usr/lib64). You should probably check your
LD_LIBRARY_PATH environment variable, and anything else that affects where shared libraries are loaded from.
P.S. You may want to take a look at this page. I must admit I only scanned it, but it sounds like /usr/lib/libz.so.1 is a symbolic link, and something about working with Mono (building MonoDevelop?) can cause this symbolic link to be re-pointed to the wrong version of libz. Check if this is what happened to you.
I can confirm that on my RHEL system, /usr/lib/libz.so.1 is a symbolic link to /usr/lib/libz.so.1.2.3:
$ ls -l /usr/lib64/libz.so.1*
lrwxrwxrwx 1 root root 13 Jun 28 2007 /usr/lib64/libz.so.1 -> libz.so.1.2.3
-rwxr-xr-x 1 root root 85928 Jul 19 2006 /usr/lib64/libz.so.1.2.3
$ ls -l /usr/lib/libz.so.1*
lrwxrwxrwx 1 root root 13 Jun 28 2007 /usr/lib/libz.so.1 -> libz.so.1.2.3
-rwxr-xr-x 1 root root 75284 Jul 19 2006 /usr/lib/libz.so.1.2.3