Fracture is an important factor that affects the oil and gas productivity of carbonate reservoirs. Much researches have been done on the origin of high-angle fractures in carbonate reservoirs, but few efforts have been made on the genetic mechanical mechanism of low-angle fractures. Based on the seismic data, core data, conventional logging data and rock mechanics experimental data, combined with three-dimensional in situ stress field simulation methods, the features, formation geological conditions and genetic mechanical mechanism of low-angle fractures (LAFs) were analyzed by applying Coulomb–Moore criterion, Griffith criterion and non-coordination criterion. The proportion of the number of shear fractures is as high as 90.2%, while that of tensile fractures is only 9.8% in the study area. Shear fractures are mainly unfilled fractures, and tensile fractures are mainly partially filled fractures. The LAFs were formed in the second tectonic movement, in which the knee-fold structure with high in the west and low in the east developed in the study area. The buried depth of most parts of the KT-I formation is 800 m when the study area develops the knee-fold structure, with a maximum depth of 1800 m and a minimum buried depth of 70 m, and the dip angle of the steepest part of the stratum is about 20°. A large number of LAFs were formed in the study area under the joint influence of tectonics and abnormally high pressure of water, including near-horizontal LAFs in the non-weak fabrics section (type I low-angle shear fractures), the LAFs having a certain angle with bedding in the non-weak fabrics section (type II low-angle shear fractures) and near-horizontal LAFs in the weak fabrics section (type III low-angle shear fractures). The formation of type I and type II low-angle shear fractures follows the Coulomb–Moore criterion. Type I low-angle shear fractures are formed in strata with a certain dip angle, while type II low-angle shear fractures are formed in near-horizontal strata. Type III low-angle shear fractures are formed under the comprehensive influence of pre-existing weak fabrics and strong horizontal extrusion, which follows the non-coordination criterion. Low-angle tensile fractures are mainly caused by abnormally high pressure and reverse faults in the study area, following Griffith’s criterion. The research in this paper not only reveals the formation mechanical mechanism of LAFs in pre-salt carbonate reservoirs but also provides guidance for the prediction of LAFs and solving the problem of water channeling caused by LAFs in oil fields.