The three hospitalised seafarers had tried to rescue their Polish compatriot after finding him unconscious in a hold containing pellets on the 503-teu Corina (built 1990) at Hanstholm on Tuesday.
They tried to provide first aid, but were themselves overcome, TV2 reported.
A 67-year-old man was confirmed dead in the incident.
The vessel is operated by Gdanska Zegluga.