Morelle tweeted that the BBC crew was shaken by the incident but that they and everyone else, including a 78-year-old woman, made it down the mountain safely.
At least six people were taken to hospitals in nearby Catania and Acireale hospitals, according to Il Corriere.
A Mount Etna eruption turned into a volcanic blast as it spewed lava and ash into the air in a visual spectacle.
In recent days Mount Etna has started spewing lava following its most recent eruption, which was on February 28 this year.
There were about 35 tourists at the volcano when flowing magma hit snow, causing the explosions, AP said, citing local authorities.
The BBC reports members of one of their teams were injured in the incident at Mt. Etna, near Sicily, and they describe the injuries as being mostly minor, including cuts and bruises. She said the experience was extremely scary.
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Lava flow mixed with steam had caused a huge explosion, which pelted the group with boiling rocks and steam, she said.
"Therefore we didn't have any serious injuries, just some small abrasions".
Morelle said the explosion was "a reminder of how unsafe (and) unpredictable volcanoes can be".
Near the east coast of Italian island Sicily, Mount Etna is over 3,000 metres tall.
Europe's grandest volcano is attracting visitors with its latest eruption.
Video filmed Wednesday shows bursts of lava and volcanic ash as the mountain exploded nearly constantly throughout the day, according to Italy's Geology and Vulcanology Institute, which published the footage.