Ginette Hemley, the group's vice president for species conservation, welcomed the company's decision, but added that Disney should work to help develop a sustainable shark fishery.
A dedicated shark fishery operated in Belize from the mid-1900s to the early 1990s, until catches of all species saw dramatic declines.
The bay was formerly the site of a basking shark fishery.
Many of these slow growing species are not recovering from overfishing by shark fisheries around the world.
The majority of shark fisheries around the globe have little monitoring or management.
The status of leopard sharks off Mexico is uncertain, although Mexican shark fisheries tend to focus more on larger species.
Because of their abundance, they form a major component of commercial and artisanal shark fisheries in many countries.
This species was once a significant part of the Cuban artisanal shark fishery, comprising 60-75% of the catch from 1937 to 1941, before its numbers dropped substantially in the 1970s.
The term probably arose in the late 1920s when the large-scale commercial shark fishery off the coast of Victoria was established.
There is an urgent need for a detailed survey of the shark fisheries of the Bay of Bengal.