The attenuation coefficients are important input values in estimating not only the dose and exposure in radiotherapy and medical imaging, but also in the proper design of photon shields. While studies are widely available above 1 keV, the attenuation coefficients of human tissues for photon energies less than 1 keV have not been studied yet. In this study, the attenuation coefficients of water and some human tissues were estimated for low energy photons using the MCNP6.1 code in the energy region 0.1 keV-1 keV. Mass attenuation coefficients were estimated at photon energies of 100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800, 850, 900, 950 and 1000 eV for water and ten human tissues (Soft, Breast, Lung, Bone, Brain, Eye lens, Ovary, Skin, Thyroid and Prostate). Results were compared with those available in literature and a fairly good agreement has been obtained. These data were then used to calculate the mean free path, half value layer, tenth value layer, effective atomic number and specific gamma-ray constant (useful for calculation of dose rate) as well. Moreover, for comparison the effective atomic number of the water has been obtained using the results of this work and using the data available in NIST database from 0.1 to 1 keV. In addition, the human tissues were compared with some tissue equivalent materials in terms of effective atomic number and specific gamma-ray constant to study the tissue equivalency from the results, the muscle-equivalent liquid with sucrose has been found to be the best tissue equivalent material for soft tissue, eye lens and brain with relative difference below 4.1%.