The crew of the Dornera were found at dawn in two rafts and a small boat, 308 nautical miles off Argentina's Patagonian coast, the Navy said in a statement.
Most of the crew are Spanish but there are also Moroccans, Peruvians and Indonesians amongst them, spokesman Enrique Balbi said.
The 25 survivors and dead sailor are aboard an Argentine fishing boat heading back to dry land and expected to arrive in Patagonia in around two days, Balbi told AFP.
To reach there, the Argentine boat must negotiate 570 kilometres of open water through a South Atlantic storm in the middle of winter, said Balbi.
The Dornera is believed to have capsized after being inundated by “a lot of water down the stern ramp where the fish nets are pulled up,” according to Balbi.
“The water entered the engine room and caused a power cut,” he said. “That made the boat uncontrollable in a storm.”
“Realizing a shipwreck was inevitable, the crew abandoned ship.” Balbi added: “At this time of year, adverse conditions created by low pressure generate a lot of wind and big waves. This can happen to any boat when there are big waves.”
Spain picked up a distress beacon and alerted the Argentine Navy, which sent out two fishing vessels to locate the sailors.
Balbi said the boat, owned by Spanish seafood company Freiremar, was fishing in international waters but that “it's still our search and rescue area”.
Two aircraft have been sent to Patagonia to help in the search and rescue operation for the missing sailor.