The interaction of proteins with an aqueous environment leads to a thin region of "biological water", the molecules of which have properties that differ from those of bulk water, in particular, reduced absorption of far-infrared radiation caused by protein-induced hindrance of the water rotational and vibrational degrees of freedom. New results at terahertz (THz) frequencies, however, show that absorption per protein molecule is increased by the presence of biological water. Absorption measurements were made of the heme protein myoglobin mixed with water from 3.6 to 98 wt % in the frequency range of 0.1-1.2 THz, using THz time-domain spectroscopy. Analysis shows greater THz absorption when compared to a non-interacting protein-water model. Including the suppressed absorption of biological water leads to a substantial hydration-dependent increase in absorption per protein molecule over a wide range of concentration and frequencies, meaning that water increases the protein's polarizability.