The animal was a male, 1.5 metres in length, and was fished in August at a depth of 700 metres, the Portuguese Institute for the Sea and the Atmosphere (IPMA) said in a statement.
Researchers from IPMA and the Centre for Maritime Sciences recorded the catching of a shark "with unusual features" by a commercial trawler, as part of an "initiative to minimise undesirable catches in European fisheries".
According to the statement, the species has "a long, slim body and a head that is reminiscent of a snake" and "its biology and ecology are little known".
The frilled shark is found across the Atlantic, including off the coast of Norway and in the waters of Scotland, Galicia in Spain, the Azores, Madeira and the Canary Islands, as well as in the Indian and Pacific Oceans, namely off Japan, Australia and New Zealand. It is rarely caught because it lives at great depths.
Fossils of the same species have been found that data back millions of years.