BBC science correspondent Rebecca Morelle tweeted to say the explosion was caused when lava flow mixed with steam.
Ms Morelle said the group, which included one 78-year-old woman, was “pelted with boiling rocks and steam”.
She said some had head injuries, burns, cuts and bruises, but added that everyone “had a very lucky escape”.
Some of the group were evacuated by a mountain rescue team, she added.
The president of the Italian Alpine Club chapter in Catania, Umberto Marino, was travelling up the volcano in a snowcat when injured people started running in his direction.
“The material thrown into the air fell back down, striking the heads and bodies of people who were closest,” Mr Marino told Catania Today.
Six people are recovering in the nearby Catania and Acireale hospitals, Il Corriere reported.
One volcanologist told Ms Morelle the explosion was the most most dangerous he had seen in his 30-year career.
“Explosions like this have killed,” she added.
“Running down a mountain pelted by rocks, dodging burning boulders and boiling steam – not an experience I ever ever want to repeat.”
Mount Etna, one of the most active volcanoes in the world, began erupting for the first time this year towards the end of last month.
It is the highest volcano in Europe at 3,330 metres and has burst into life several times each year.Reuse content