Moussaka can be frozen in a freezer safe, airtight container, and kept for up to 3 months. Thaw the moussaka overnight in the refrigerator, then cover with aluminum foil and reheat in a 350 degree oven until hot throughout. Refrigerator Storage: Store leftover moussaka in the refrigerator, in an airtight container, for up to 5 days. Reheat in the microwave or the oven until warmed through.