Catalyzes the NAD(H)-dependent interconversion of D-fructose 6-phosphate and D-mannitol 1-phosphate in the mannitol metabolic pathway. D-mannitol 1-phosphate + NAD(+) = beta-D-fructose 6-phosphate + H(+) + NADH Monomer. Belongs to the mannitol dehydrogenase family.