The incident happened on the 179,000-dwt Hanjin Sines (built 2009) on Wednesday at the port of Ferrol, local media said.
The victim was a 56-year-old local man, Antonio Diaz Pinol.
Emergency services were alerted, but could not save the dock worker.
Police are considering the possibility that he died from asphyxiation or a fall, or a combination of both.
The vessel is listed as operated by H-Line Shipping of South Korea.