The incident took place Friday night on the ship Zelada Degagnes.
A Cormorant helicopter and Hercules plane were also sent from Newfoundland and Nova Scotia to help with the rescue.
Capt. Denis Coulombe said the call came in around 10 a.m., and that rescuers arrived at the ship located near Cumberland Sound at about 7 p.m.
Coulombe said the supply ship did not have a helicopter landing pad so the patient had to be lowered into a zodiac inflatable boat and transported across the water to the Coast Guard ship.
"The patient was not in a so bad condition," said Coulombe. "He was still on his feet, he was able to walk, he was conscious."
Coulombe added that the Cormorant helicopter flew the patient to hospital in Iqaluit, about an hour away, around midnight.
The DesGroseilliers is one of six Coast Guard ships currently patrolling the Arctic.