To provide a hydrogen generating apparatus that efficiently generates hydrogen from ammonia, and a fuel cell system that generates power using the efficiently generated hydrogen. A hydrogen generating apparatus (1) is provided with a plasma reactor (3), a high-voltage electrode (5), a grounding electrode (7), and a gas supply means (15) that supplies a gas containing ammonia to the plasma reactor. The high-voltage electrode (5) is configured with a hydrogen separation membrane (12) included therein. Under the conditions of room temperature and atmospheric pressure, the hydrogen separation membrane (12) of the high-voltage electrode (5) discharges electricity between the grounding electrode (7) and the hydrogen separation membrane with power supplied from a high-voltage pulse power supply (2), and hydrogen is generated by bringing into the plasma state the ammonia contained in the gas thus supplied.