In the last decade, the negative impact of hydraulic fracturing fluids on the reservoir properties has been noted, which has led to the new trend of improving characteristics and developing new hydraulic fracturing fluids. As an alternative option to the traditionally used cross-linked fluids based on guar solution, in our laboratory we have tested fluids having a branched spatial structure, which allowed them to hold and transport proppants, despite the low viscosity of this kind of fluids (100–200 mPa·s measured at 100 s−1). Existing theoretical models of hydraulic fracture (HF) propagation have some limitations in predicting the influence of fracturing fluids on reservoir properties. Unfortunately, in situ experiments in the target reservoir are difficult and expensive. Thus, laboratory experiments can be considered as a reasonable alternative for testing new fluids, since they can provide comprehensive information about the properties of the created HF before the application of a new hydraulic fracturing technique in the field conditions. This paper presents the results of an experimental study of hydraulic fracturing of granite samples in laboratory conditions. The injection of water- and oil-based unconventional fracturing fluids was performed to study the influence of fluid rheology on the dynamics of the hydraulic fracture propagation process and parameters of the created HF. We have found that the fracturing fluid viscosity affects the parameters of the created HF, such as aperture, propagation velocity, breakdown pressure, and HF surface tortuosity. The obtained relationships can be taken into account for Hydraulic Fracture modelling, which may increase the efficiency of the hydraulic fracturing in the field conditions.