One of Greece's top seismologists is under investigation over an April Fool's joke warning that a huge "funnel" could open up under the popular tourist destination Santorini island.

Akis Tselentis, the director of Greece's Geodynamic Institute and Tsunami Center, on Wednesday posted on Facebook a photo of himself in a mock mugshot pose, holding a sign that read "guilty of April Fool's joke".

"We live in a country where humour is persecuted," he added.

On Tuesday, a prosecutor ordered a preliminary investigation to determine whether Tselentis' April 1 posting qualified as spreading false news.

"Things are not well regarding Santorini," Tselentis had said.

"From January onwards we have a gradual disappearance of magma beneath the volcano," the April Fool's post said.

Tselentis said there was a "major possibility" that magma would shift towards a fictional volcano, leaving a funnel vacuum that would "suck the waters of the Aegean".

Santorini was completely reshaped by a volcanic eruption in the late 17th century BCE that wiped out a culturally advanced Minoan colony, and geothermal activity accompanied by seismic tremors remains high to this day.

The last major eruption of the most active part of the volcano, beneath the uninhabited black lava islet of Kameni near Santorini, occurred in 1950.