Near-wellbore damage, which significantly reduces hydrocarbon production, can happen during drilling, cementing, perforation, completion, and stimulation operations. The most common technique to remove or bypass this damage is matrix acidizing. The effects of matrix acidizing injection pressure on acid penetration rate, chemical reaction rate, solubility, porosity, and permeability of Marcellus core samples were investigated in this experimental study. To achieve a successful acid treatment, acid type and concentration must be carefully selected. The results of the X-ray powder diffraction (XRD) and the solubility test revealed that 15 wt.% hydrochloric acid (HCl) is the optimum acid. Matrix acidizing treatments were implemented on nine core samples, taken from Marcellus (shale gas reservoir), at the reservoir temperature (66 °C), confining pressure of 10.35 MPa, and three different acid injection pressures (1.72, 3.45, and 5.17 MPa). The results showed that performing acid treatments on the samples containing continuous carbonate layers created highly permeable channels (wormholes) resulting in significant improvement, up to 3900%, in the permeability of the samples. Additionally, the results of the acid penetration rate, chemical reaction rate, solubility, porosity, and permeability revealed that increasing the acid injection pressure resulted in increases in the aforementioned properties of the samples. The results also revealed that any increase in the injection pressure above 3.45 MPa did not demonstrate any significant enhancements in the properties of the samples. The results of the XRD analysis revealed that matrix-acidizing treatments dissolved 23.2% of calcite and 0.4% of dolomite existed in the samples.