Japanese whalers in the past opportunistically caught Cuvier's, taking between three and 35 each year (before 1955).
The species has been reported taken incidentally in fisheries in Colombia, the Italian swordfish fishery, and in the drift gillnet fishery off the U.S. west coast, where between 22 and 44 individuals died each year off California and Oregon from 1992 to 1995.
Cuvier's beaked whale is covered by the Agreement on the Conservation of Small Cetaceans of the Baltic, North East Atlantic, Irish and North Seas (ASCOBANS) and the Agreement on the Conservation of Cetaceans in the Black Sea, Mediterranean Sea and Contiguous Atlantic Area (ACCOBAMS).
The species is further included in the Memorandum of Understanding Concerning the Conservation of the Manatee and Small Cetaceans of Western Africa and Macaronesia (Western African Aquatic Mammals MoU) and the Memorandum of Understanding for the Conservation of Cetaceans and Their Habitats in the Pacific Islands Region (Pacific Cetaceans MoU).

Beaked whales may also be sensitive to noise: a higher incidence of strandings has been recorded in noisy seas such as the Mediterranean, and multiple mass strandings have occurred following operations by the Spanish Navy in the Canary Islands.
In 2019, a review of evidence on the mass strandings of beaked whale linked to naval exercises where sonar was used was published.
It concluded that the effects of mid-frequency active sonar are strongest on Cuvier's beaked whales but vary among individuals or populations, and the strength of the whales' response may depend on whether the individuals had prior exposure to sonar.
The report considered that the most plausible explanation of the symptoms of decompression sickness such as gas embolism found in stranded whales to be the whales' response to sonar.
 It noted that no more mass strandings had occurred in the Canary Islands once naval exercises where sonar was used were banned there, and recommended that the ban be extended to other areas such as the Mediterranean where mass strandings continue to occur.
Japanese whalers in the past opportunistically caught Cuvier's, taking between three and 35 each year (before 1955). The species has been reported taken incidentally in fisheries in Colombia, the Italian swordfish fishery, and in the drift gillnet fishery off the U.S. west coast, where between 22 and 44 individuals died each year off California and Oregon from 1992 to 1995. Cuvier's beaked whale is covered by the Agreement on the Conservation of Small Cetaceans of the Baltic, North East Atlantic, Irish and North Seas (ASCOBANS) and the Agreement on the Conservation of Cetaceans in the Black Sea, Mediterranean Sea and Contiguous Atlantic Area (ACCOBAMS). The species is further included in the Memorandum of Understanding Concerning the Conservation of the Manatee and Small Cetaceans of Western Africa and Macaronesia (Western African Aquatic Mammals MoU) and the Memorandum of Understanding for the Conservation of Cetaceans and Their Habitats in the Pacific Islands Region (Pacific Cetaceans MoU).
Beaked whales may also be sensitive to noise: a higher incidence of strandings has been recorded in noisy seas such as the Mediterranean, and multiple mass strandings have occurred following operations by the Spanish Navy in the Canary Islands. In 2019, a review of evidence on the mass strandings of beaked whale linked to naval exercises where sonar was used was published. It concluded that the effects of mid-frequency active sonar are strongest on Cuvier's beaked whales but vary among individuals or populations, and the strength of the whales' response may depend on whether the individuals had prior exposure to sonar. The report considered that the most plausible explanation of the symptoms of decompression sickness such as gas embolism found in stranded whales to be the whales' response to sonar.  It noted that no more mass strandings had occurred in the Canary Islands once naval exercises where sonar was used were banned there, and recommended that the ban be extended to other areas such as the Mediterranean where mass strandings continue to occur.
Cuvier's beaked whale