Catalyzes the reversible oxidation of malate to oxaloacetate. Can use both NAD and NADP for malate oxidation, but NADPH cannot be used for oxaloacetate reduction. (S)-malate + NAD(+) = H(+) + NADH + oxaloacetate Strongly inhibited by iodoacetic acid and CuCl(2). Completely inhibited by N-ethylmaleimide and HgCl(2). kcat is 138 sec(-1). Optimum pH is 10.5 for malate oxidation and 8.0 for oxaloacetate reduction. Optimum temperature is 40 degrees Celsius. Homotetramer. Belongs to the LDH/MDH superfamily. MDH type 3 family.