In the present paper, we concentrate on the heterogeneous cement mortars and we treat them as Cosserat-based media. The autogenous shrinkage phenomenon at early age (from 1 up to 3 days after mixing) has been analyzed by means of Cosserat theory. The characteristic length scale parameter Lc in this theory helps us to change the size specimen from macro-scale to micro-scale using the theoretical size effect aspects. This methodology is also capable of treating cracks initiation and their appearance in the cementitious matrix surrounding the sand-inclusions, which should occurred inside of the Representative Volume Elementary (RVE) of mortar subjected to self-desiccation shrinkage during hydration at early age. By taking advantage of the Nonlinear Finite Element Analysis (NFEA), the numerical experiments have been performed. The numerical outcomes are well agreed with the experimental observations coming from Scanning Electronic Microscopy (SEM) images. It concludes that the inclusions create not only a hygro stress concentration around the grains but also the number of inclusions should influence the network in cementitous matrix.