This study aimed to investigate the effect of the microstructure of shale on fracture initiation and extension during hydraulic fracturing. The Longmaxi Formation shale reservoir in the Sichuan Basin was considered as the research object; its structure was modeled from a microscopic perspective, and a zero-thickness cohesive unit was embedded within the solid unit. Numerical simulations were performed to study the effect of mineral content on the microextension of the hydraulic fracture, extension behavior, and evolution law of shale. The results showed that changes in the mineral content resulted in changes in the forces between molecules within the minerals, which, in turn, affected the shale's brittleness. The percentages of brittle mineral content in the Long I, II, and III reservoir sections are 60.37, 47.60, and 53.56%, respectively. The fracture initiation pressures of the three reservoirs were 29.22, 31.42, and 30.22 MPa, respectively, and a linear correlation was found between the fracture initiation pressures and the brittle mineral contents of the reservoir sections. An increase in the reservoirs' percentage of brittle mineral content facilitated the fracture initiation, with a corresponding gradual decrease in the resistance to fracture initiation. The pore pressures of the fractures in the three reservoirs after fracture initiation were 0.90, 1.18, and 1.00 MPa, respectively. The larger the percentage of brittle minerals was, the lower was the fracture pore pressure. The greater the length, number, area, and width of the cracks were, the more likely they were to form longer and wider cracks. Hence, reservoirs with a high percentage of brittle minerals should be prioritized as the target formations for hydraulic fracturing operations. The results of this study reveal how the mineral content affects the extension of microscopic hydraulic fractures in shale reservoirs. As such, this work can provide a theoretical basis for rationally selecting a hydraulic fracturing operation layer in shale gas reservoirs.