With the increasing applications of nuclear technology, radiation protection has become very important especially for the environment and the personnel close to radiation sources. Natural clays can be used potentially for shielding the X-ray radiations. In this study, the correlation between structural parameters and radiation shielding performance of natural clay extracted from Algerian Sahara (Adrar, Reggan, and Timimoune) was investigated. Phase composition and structural parameters (lattice parameters, average crystallite size, and microstrain) were determined by the Rietveld refinements of X-ray diffraction patterns in the frame of HighScore Plus software. The obtained results showed that the studied clays are nanocrystalline (nano-clay) since the calculated crystallite size was ≈3 nm for the feldspar phase. FTIR spectra confirmed the presence of all phases already detected by XRD analysis besides Biotite (around the band at 3558 cm−1). The remaining bands corresponded to absorbed and adsorbed water (3432 cm−1 and 1629 cm−1, respectively) and atmospheric CO2 (2356 cm−1). The shielding properties (mass absorption coefficient—µ/ρ and radiative attenuation rate—RA) for (green-yellow, green, and red) clays of Adrar, (red, white, and white-red) clays of Reggan, and red clay of Timimoune at same energy level were examined. The results of clay samples were compared with each other. The obtained results indicated that the green clay of Adrar exhibited the superior radiation shielding, i.e., 99.8% and 243.4 cm2/g for radiative attenuation rate and mass absorption coefficient, respectively.