Make distutils look for numpy header files in the correct place

Use numpy.get_include():

from distutils.core import setup
from distutils.extension import Extension
from Cython.Distutils import build_ext
import numpy as np                           # <---- New line

ext_modules = [Extension("hello", ["hello.pyx"],
                                  include_dirs=[get_numpy_include()])]   # <---- New argument

setup(
  name = 'Hello world app',
  cmdclass = {'build_ext': build_ext},       
  ext_modules = ext_modules
)

The answer given by @vebjorn-ljosa is correct, but it causes problems when used in conjunction with install_requires=['numpy']. In this situation, your setup.py needs to import numpy, which will cause an error if you try to pip install your project without running pip install numpy first.

If your project depends on numpy, and you want numpy to be installed automatically as a dependency, you need to set include_dirs only when your extensions are actually being built. You can do this by subclassing build_ext:

from distutils.core import setup
from distutils.extension import Extension
from Cython.Distutils import build_ext

class CustomBuildExtCommand(build_ext):
    """build_ext command for use when numpy headers are needed."""
    def run(self):

        # Import numpy here, only when headers are needed
        import numpy

        # Add numpy headers to include_dirs
        self.include_dirs.append(numpy.get_include())

        # Call original build_ext command
        build_ext.run(self)

ext_modules = [Extension("hello", ["hello.pyx"])]

setup(
  name = 'Hello world app',
  cmdclass = {'build_ext': CustomBuildExtCommand},
  install_requires=['numpy'],
  ext_modules = ext_modules
)

And you can use a similar trick to add cython as an automatically installed dependency:

from distutils.core import setup
from distutils.extension import Extension

try:
    from Cython.setuptools import build_ext
except:
    # If we couldn't import Cython, use the normal setuptools
    # and look for a pre-compiled .c file instead of a .pyx file
    from setuptools.command.build_ext import build_ext
    ext_modules = [Extension("hello", ["hello.c"])]
else:
    # If we successfully imported Cython, look for a .pyx file
    ext_modules = [Extension("hello", ["hello.pyx"])]

class CustomBuildExtCommand(build_ext):
    """build_ext command for use when numpy headers are needed."""
    def run(self):

        # Import numpy here, only when headers are needed
        import numpy

        # Add numpy headers to include_dirs
        self.include_dirs.append(numpy.get_include())

        # Call original build_ext command
        build_ext.run(self)

setup(
  name = 'Hello world app',
  cmdclass = {'build_ext': CustomBuildExtCommand},
  install_requires=['cython', 'numpy'],
  ext_modules = ext_modules
)

Note: these approaches only work with pip install .. They won't work for python setup.py install or python setup.py develop as in these commands cause dependencies to be installed after your project, rather than before.