The 10 suffered minor burns, cuts and bruises and six were hospitalised.
German volcanologist Boris Behncke described on his Facebook page how the explosion was triggered by a build-up of steam after molten lava overran a layer of snow. "I received a bruise on the head but I am fine," said the Etna specialist.
The explosion occurred at 12.43pm (1143 GMT) when the steam trapped between the lava and the surface of the mountain escaped in a powerful burst, Stefano Branca, of the Italian institute of geology and volcanology (INGV), told AFP.
BBC science correspondent Rebecca Morelle tweeted that it could easily have been much worse.
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"Everyone taken off the mountain - rescue team and guides here were brilliant," she wrote on Twitter, adding: "BBC team all ok - some cuts/ bruises and burns. Very shaken though - it was extremely scary."
Morelle said a volcanologist with them on the peak described the incident as the most dangerous in his 30-year career.
"Running down a mountain pelted by rocks, dodging burning boulders and boiling steam - not an experience I ever ever want to repeat.
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