A video shows the huge sea creature, slowly moving towards the vessel from which it's being filmed, its fin occasionally popping up as it gets closer and closer.
The clip was filmed by Salvatore Sicurello, who was sailing on the boat while it was just off the coast of the south of Italy, near Lampedusa - one of the Pelagie Islands in the Mediterranean Sea
After it was uploaded to Facebook on 23 May, it's been shared and viewed thousands of times.
Mr Sicurello thinks the shark he saw was around 20 feet long, but social media users were in debates over whether it was a great white or not.
Shark expert Patrick Jambura, a researcher at the University of Vienna, questioned whether it could be a mako shark in the clip.
He said: "This video of a supposed great white shark, Carcharodon carcharias, was taken in front of Lampedusa.
"The verification of the species is still pending, since makos and white sharks can look very similar and we do not want to jump to conclusions here."
But after analysing Mr Sicurello's video, he said he was confident it was in fact a great white shark.
He later said: "So far we have corresponded with some colleagues with the result that it is really a great white shark."
The great white shark is considered the most voracious apex predator in temperate marine ecosystems anywhere in the world.
They can measure up to 20 feet in length and weigh up to 5,000 pounds (2,250 kg).
The great whites can reach a speed up to 15 miles/hour (24 km per hour).
It's not the first time in recent weeks that a shark has been spotted in the Med.
A swimmer came face to face with a basking shark, just off the coast of Malaga, Spain. The monstrous animal glided past him, with its fin peeking out of the water.
According to reports, this most recent sighting (22 May) of the the plankton-eating basking shark was the third in less than a month in the country's southern waters.
Experts who have seen the footage believe that the shark was about 20ft long.
It's understood that the video was captured from a boat the swimmer is thought to have jumped from in order to get a closer look at the animal.
And though the shark is said to be harmless to humans, local authorities have warned kayakers and other sports enthusiasts to be vigilant and not to approach them.
This comes after another shark of the same sort described as being more than 26ft long was spotted a few weeks back (16/17 May), off La Mamola Beach.