It is shown that an isothermal shock wave can occur in liquid water just below its temperature of maximum density. Thermodynamic functions previously obtained by Thomsen and Hartka are used to obtain an explicit solution of the Hugoniot relation under isothermal conditions; the resulting entropy increase is also computed. Such a shock takes place between a state in the anomalous region (negative coefficient of thermal expansion) and one in the normal region (positive coefficient). For the most part, properties of the shock wave are similar to the usual cases; certain anomalies are briefly discussed. The results apply qualitatively to any other fluids with similar properties, if such exist.