Italian news reports say scientists investigating the recent eruptions were injured when magma spewing from the volcano hit snow, causing an explosion.
Mount Etna is one of Europe's most active volcanoes, and had begun erupting on the morning of March 15.
Morelle said the explosion caused head injuries, burns, cuts and bruises, adding that one volcanologist had told her it was the most unsafe incident he had experienced in a 30-year career.
According to Italian news agency ANSA, four people including three German tourists were hospitalised, mostly with head injuries - though none of the injuries was listed as grave. "Volcanologist said most risky incident experience in his 30 year career", read another tweet from Morelle.
The BBC crew were at the scene to witness the spectacle, and although they suffered cuts, bruises and burns, they were physically well.
Morelle said all those involved in the eruption were "okay" and had been brought of the mountain safely by an "excellent rescue team".
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Among the injured include a BBC journalist and her film crew, and a 78 year old woman.
"Explosions like this have killed", she said.
She added that a "huge explosion" caused rocks and steam to be pelted at the group.
Officials at Sicily's Catania airport announced they would reduce arrivals by half to five flights an hour, due to ash clouds.
Fortunately, she said, everyone at the volcano escaped with their lives and without serious injuries.
A BBC team and some tourists were on the mountain when the explosion happened.