Catalyzes the reversible oxidation of malate to oxaloacetate. (S)-malate + NAD(+) = H(+) + NADH + oxaloacetate Optimum pH is 9.5-10.0 for malate dehydrogenation, and 7.5-8.0 for oxaloacetate reduction. Optimum temperature is 40 degrees Celsius. Homodimer. Belongs to the LDH/MDH superfamily. MDH type 1 family.