In this work we carefully analyze the role of the microstructure on the magnetic properties of Co-doped ZnO nanoparticles prepared by the vaporization-condensation method in a solar reactor. We show that a close correlation exists between microstructural features and the appearance of ferromagnetism. Both shape and size of the particles, as well as the microstructure, can be controlled by changing the pressure inside the evaporation chamber, as evidenced by transmission electron microscopy micrographs and high resolution electron microscopy (HREM). X-ray diffraction patterns and HREM make evident the absence of any significant Co segregation or any other phase different from wurtzite type ZnO. On the other hand, electron energy loss spectroscopy analyses performed on several particles of wurtzite type ZnO yielded an average Co concentration in good agreement with the nominal composition. Samples prepared in low pressure (approximate to 10 Torr) exhibit a very homogeneous microstructure and are ferromagnetic at low temperature but they have a very small saturation moment, well below that expected for a Co2+ ion. Conversely, samples prepared at higher pressure conditions (approximate to 70-100 Torr) show a defective microstructure and are paramagnetic and increasing the Co content does not induce ferromagnetism.