"The shark was pretty close to us [...] And in fact my fingers were trembling when I was trying to get the camera operating," volunteer diver Derk Remmers told the BBC.
It is thought overfishing has contributed to driving the species to near extinction in the Mediterranean.
Scientists say people should not be concerned as the shark, believed to be an adult male, was spotted many miles offshore between Tunisia and Sicily.
Conservationists said they hoped the sighting may encourage governments to create marine protected areas in Mediterranean waters.
Divers working for the NGO Healthy Seas captured the footage whilst diving to highlight the problem of so-called "ghost fishing nets".
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