According to German Press Agency (dpa), a group of 25 tourists was visiting the Breiðamerkurjökull glacier as part of a guided tour when the cave collapsed.
Dozens of rescue workers were deployed, including specialised cave rescuers and two helicopters.
A spokeswoman for the authorities said that the conditions at the scene of the accident were extremely difficult.
Breiðamerkurjökull, located in the south-east of the country, is a glacial tongue that extends from southern Vatnajökull into the glacier lagoon Jökulsárlón.
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