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Nondissociative, magnetohydrodynamic, C-type shock waves are expected to be a prodigious source of far- infrared water emissions in dense interstellar regions. We have constructed a model to calculate the far- infrared H<SUB>2</SUB>O line spectra that emerge from such shocks. Using the best estimates currently available for the radiative cooling rate and the degree of ion-neutral coupling within the shocked gas, we modeled the temperature structure of MHD shocks using standard methods in which the charged and neutral particles are treated separately as two weakly coupled, interpenetrating fluids. Then we solved the equations of statistical equilibrium to find the populations of the lowest 179 and 170 rotational states of ortho and para-H<SUB>2</SUB>O. We have completed an extensive parameter study to determine the emergent H<SUB>2</SUB>O line luminosities as a function of preshock density in the range n(H<SUB>2</SUB>) = 10<SUP>4</SUP>-10<SUP>6.5</SUP> cm<SUP>-3</SUP> and shock velocity in the range ν<SUB>s</SUB> = 5-40 km s<SUP>-1</SUP>. We find that numerous rotational transitions of water are potentially observable using the Infrared Space Observatory and the Submillimeter Wave Astronomy Satellite and may be used as diagnostics of the shocked gas. We have also computed the rotational and ro-vibrational emissions expected from H<SUB>2</SUB>, CO, and OH, and we discuss how complementary observations of such emissions may be used to further constrain the shock conditions. In common with previous studies, we come close to matching the observed H<SUB>2</SUB> and high-J CO emissions from the Orion-KL star-forming region on the basis of a single shock model. We present our predictions for the strengths of H<SUB>2</SUB>O line emission from the Orion shock, and we show how our results may be scaled to other regions where molecular shocks are likely to be present.