An ice-full state detecting apparatus and a refrigerator having the same are disclosed. The refrigerator including an ice-full state detecting apparatus includes: a refrigerator body including a cooling chamber; a cooling chamber door to open and close the cooling chamber; an ice maker installed at the cooling chamber or at the cooling chamber door; an ice storage container to store ice made by the ice maker; and the ice-full state detecting apparatus to detect an ice-full state of the ice storage container, wherein the ice-full state detecting apparatus includes: a ice-full state detecting sensor to detect an ice-full state of the ice storage container; a sensor heater to heat the ice-full state detecting sensor; a detecting unit to detect whether the ice-full state detecting sensor is in contact with external air; and a controller to control the operation of the sensor heater based on the detection result of the detecting unit. The ice-full state detecting sensor can be restrained from being frosted to thus prevent degradation of detection performance of the ice-full state detecting sensor. In addition, power consumption required for a defrosting operation can be reduced.