Thermal rectification in nanostructured materials is an active topic of research and development. Here it is suggested that porous semiconductor materials can offer an unmatched tailoring of its structural properties, resulting in both the ability to study the effects of nanoscale morphology on thermal rectification phenomenon, and the perspective to achieve large thermal rectification over a wide temperature range in combination with other beneficial properties, such as a wide tunability of thermal conductivity, or optical transparency of the thermally rectifying structure. In this contribution we are presenting the first to our knowledge experimental demonstration of thermal rectification in mesoporous silicon. The influence of pore morphology controlled via Si substrate crystallographic orientation and etching conditions on thermal rectification are studied. The effect of oxidation of the porous material is presented as well. Experimental results are further compared with several recently published theoretical predictions of thermal rectification in similar structures.