I found a good blog post that provides another solution that worked in my case:
http://linfiniti.com/2013/02/installing-python-gdal-into-a-python-virtualenv-in-osx/
The only difference to the blog post is that I had to do is to download the correct version of GDAL that matched the kyngchaos packages. In my case I was using the GDAL framework version 1.10, so the following install was successful
source venv/bin/activate
pip install --no-install GDAL==1.10.0
cd venv/build/GDAL
python setup.py build_ext\
--gdal-config=/Library/Frameworks/GDAL.framework/Versions/1.10/unix/bin/gdal-config\
--library-dirs=/Library/Frameworks/GDAL.framework/Versions/1.10/unix/lib/\
--include-dirs=/Library/Frameworks/GDAL.framework/Versions/1.10/Headers/
Then leave the GDAL directory and install without download
cd ~
pip install --no-download GDAL
UPDATE: You might have to add some env vars before calling setup.py for the compilation step to work (see this questionsee this question)
export CFLAGS=-Qunused-arguments export CPPFLAGS=-Qunused-arguments