The 5-metre great white, its fin clear to see, repeatedly weaved from side to side as the researchers watched it in awe.
“We saw a black fin and straight away could see it was a very big shark,” cameraman Fernando Lopez-Mirones told El Pais.
“The conditions in the sea were amazing and we had the specimen around three metres from the boat, and we could watch it up close for 70 minutes.”
The Spanish scientists, who were researching marine life in the area, said first sighting in more than three decades of a great white was “historic”.
Although the sharks are native to the Mediterranean, they are normally associated with the oceans off South Africa, Australia and the US.
The first officially recorded sighting in the Mediterranean for at least 30 years excited the research team because the creatures – which can bite humans who get too close – are officially at risk of extinction.
From the 1920s to the 1970s, 27 great whites were captured in the region, according to a 2003 scientific report, but numbers are thought to have plummeted since, because of overfishing, accidental trapping in discarded nets and demand for shark fin soup in the far East.
Mr Lopez-Mirones and colleagues on board an expedition off the Balearics – including Briton Georgina Stevens – are researching the effects of microplastics pollution, among other things.