I found the solution in a blog: I had to build a symbolic link and set an environment variable. This is my working code:
apt-get install zlib1g-dev
cd /lib
sudo ln -s i386-linux-gnu/libz.so.1 libz.so
mkdir /tmp/shell_scripts
cd /tmp/shell_scripts
wget http://www.python.org/ftp/python/2.6.9/Python-2.6.9.tgz
tar -xvzf Python-2.6.9.tgz
rm Python-2.6.9.tgz
cd Python-2.6.9
make distclean
export LDFLAGS="-L/usr/lib/$(dpkg-architecture -qDEB_HOST_MULTIARCH)"
./configure
make
make install
./python setup.py install
unset LDFLAGS
cd /tmp
rm -r shell_scripts
Now, import zlib
no longer throws an error.