In this study, a set of laboratory experiments was carried out to study the parameters of hydraulic fractures induced in the dry and mineral-oil-saturated rocks and compare them with the geomechanical characteristics of tested samples. We chose sandstone and thermally treated granite as the materials for research. There are very few known studies related to the mechanical and acoustic properties of oil-saturated rocks, and even fewer studies describing, in detail, the parameters of hydraulic fractures generated in oil-saturated rocks. The hydraulic fracture parameters were determined using a set of independent sensors installed to measure the axial deformation of the sample (which is directly related to the aperture of created hydraulic fracture), fluid pressure, fluid volume injected into hydraulic fracture, and localization of acoustic emission (AE) events, generated during the propagation of hydraulic fractures. Our study focuses on the investigation of the influence of rock properties, altered by mineral oil saturation and thermal treatment, on such parameters of hydraulic fracturing as breakdown pressure (BP), fracture aperture, and the resulting roughness of the hydraulic fracture surface. In addition, we studied the influence of injected fluid viscosity on the parameters of created hydraulic fractures. It was revealed that the saturation state caused a reduction in the values of mechanical parameters such as Young’s modulus, compressive strength, and cohesion, and had a similar reducing influence on the breakdown pressure. The values of HF parameters, such as fracture width and the volume of fracturing agent injected into the HF, are higher in the tests for both saturated sandstone and saturated TT granite. However, we found out that thermal treatment of granite samples led to a much more significant reduction in the values of mechanical and acoustic parameters than the mineral-oil saturation procedure because it created a dense network of thermally induced cracks. The results obtained in our laboratory studies can be taken into account in the modeling of hydraulic fracturing in the field.