Crustal magnetic fields on Mars are inhomogeneously distributed with the strongest fields occurring over the southern highlands in a longitude sector between approximately 130¿E and 240¿E. Using analytic approximations and empirical scaling laws, it is estimated that much of the weakly magnetized southern highlands (i.e., that between 110¿W and 130¿E) was shocked to pressures exceeding 1--2 GPa during the Hellas and Argyre impacts. Possible primary remanence carriers in the martian crust include iron oxides and iron sulfides (pyrrhotite). If pyrrhotite is the main remanence carrier, extensive demagnetization of crustal regions (~90%) may occur at shock pressures of 2 GPa or more. Thus, at least for this remanence carrier, impact shock demagnetization can potentially explain the distribution of crustal fields in the southern highlands.