Among those near the summit of Mount Etna when it began to erupt was a 76-year-old woman who was able to rush to safety.
On Twitter Morelle said: "Caught up in incident at Mount Etna - BBC crew & tourists caught up in huge explosion - caused injuries and evacuation from scene".
BBC science reporter Rebecca Morelle tweeted: "Many injured - some head injuries, burns, cuts and bruises".
One volcanologist told the BBC that this latest eruption from Etna, one of the most active volcanoes on the planet, was the most risky he had seen in 30 years.
She added: "Bbc team all ok - some cuts/ bruises and burns".
Etna, Europe's tallest active volcano, has shown lava spouts and ash plumes in recent days.
The president of the Italian Alpine Club chapter in Catania, Umberto Marino, said he was travelling up the volcano in a snowcat when injured people started running in his direction.
So far it has not disrupted traffic at the nearby Catania airport or created inconvenience for residents in the area.
Morelle said all those involved in the eruption were "okay" and had been brought of the mountain safely by an "excellent rescue team".
Thursday's volcanic blast, which caught out the BBC group, caused lava to ooze down the southern side of the crater, according to Italy's National Institute of Geophysics and Volcanology. "There were 10 injuries but none serious", he said.
The red hot lava flowing from Mount Etna can be seen clearly in the image from Sentinel-2A.