Khaled Mahfoudh Bahah, Yemen's oil minister, said several earthquakes were felt on the island on Sunday which triggered the eruption.
Ali Abdullah Saleh, the Yemeni president, gave instructions to Yemen's navy to send rescue teams to the island, state news agency Saba said.
Ken Allan, a Canadian navy spokesman, said a Nato fleet just outside the territorial waters of the island reported seeing a "catastrophic volcanic eruption" at 7pm (16:00 GMT) on Sunday.
"At this time, the entire island is aglow with lava and magma as it pours down into the sea. We do not have confirmation of how many people were on this island at the time of the eruption," Allan said in an email.
"The lava is spewing hundreds of feet into the air, with the volcanic ash also [rising] a thousand feet in the air."
Saba said a military garrison on the island was being evacuated.
The Canadian armed forces said it was trying to locate nine people believed to be at sea after Yemen's coast guard requested help.
The Nato fleet was sailing towards the Suez Canal when it spotted the eruption. The government of Yemen asked Nato to assist in the search for survivors and the closet ship, the HMCS Toronto, is heading towards the island.