Correlations between chemical and structural complexities of minerals were analysed using a total of 4962 datasets on the chemical compositions and 3989 datasets on the crystal structures of minerals. The amounts of structural and chemical Shannon information per atom and per unit cell or formula unit were calculated using the approach proposed by Krivovichev with no H-correction for the minerals with unknown H positions. Statistical analysis shows that there are strong and positive correlations (R2 > 0.95) between the chemical and structural complexities and the number of different chemical elements in a mineral. Analysis of relations between chemical and structural complexities provides strong evidence that there is an overall trend of increasing structural complexity with the increasing chemical complexity. Following Hazen, four groups of minerals were considered that represent four eras of mineral evolution: “ur-minerals”, minerals from chondritic meteorites, Hadean minerals, and minerals of the post-Hadean era. The analysis of mean chemical and structural complexities for the four groups demonstrate that both are gradually increasing in the course of mineral evolution. The increasing complexity follows an overall passive trend: more complex minerals form with the passage of geological time, yet the simpler ones are not replaced. The observed correlations between the chemical and structural complexities understood in terms of Shannon information suggest that, at a first approximation, chemical differentiation is a major force driving the increase of complexity of minerals in the course of geological time. New levels of complexity and diversification observed in mineral evolution are achieved through the chemical differentiation, which favours local concentrations of particular rare elements and creation of new geochemical environments.