An explosion sent rocks and debris hurtling through the air and through the roof of the tourist vessel.
One passenger broke a leg while others suffered burns. The authorities are investigating.
The lava is from Hawaii's Kilauea volcano, which erupted in May and has been spewing out gas and molten rock ever since.
The explosion left a gaping hole in the roof of the tour boat, which had been taking visitors out to view lava plunging into the sea.
Those injured are being treated in hospital.