In this paper, we present the results of compositional analysis of a copper-rich mineral known as malachite, collected from the Gilgit-Baltistan region of Pakistan. A calibration-free laser-induced breakdown spectroscopy (CF-LIBS) technique is employed for determination of elemental composition of the sample. The study aims at the investigation of the presence of precious elements, if any, in minerals of local origin. The laser beam of a 1064 nm wavelength from a nanosecond pulsed $Q$Q-switched Nd:YAG laser was focused on the surface of the sample, and an emission spectrum was obtained with the help of a LIBS2000 spectrometer covering the spectral range between 200 to 700 nm. Results obtained through analyzing the characteristic emission lines of different elements have confirmed the presence of sixteen (16) elements in the investigated sample, viz. Cu, Si, Al, K, Fe, Mn, Ag, Ti, Ba, Sr, Ca, Mg, Na, Li, C, and H. For quantification of the detected elements in the sample, a calibration-free method based on local thermodynamic equilibrium and optically thin plasma model was employed. Plasma parameters, such as electron number density and temperature, were calculated for the purpose of subsequent calculations. Seven elements, viz. Cu, Fe, Si, Ca, Mg, Mn, and Al, were quantified out of 16 initially detected elements, and their concentration in terms of weight percentage was 43.15%, 20.13%, 18.31%, 9.46%, 3.28%, 3.16%, and 2.51%, respectively. The presence of all seven elements quantified by CF-LIBS was confirmed by x-ray fluorescence analysis.