"We are sad to inform that one of the three patients The Alfred received from the volcano tragedy has passed away," Efe news quoted Melbourne's Alfred Hospital as saying in a statement.
"Two patients continue to receive specialist burns care. One is in a stable condition. One is in a critical condition," it added.
The victim was one of 12 injured people evacuated to hospitals in Australia and the second in this group to die.
New Zealand Police Deputy Commissioner John Tims confirmed in a statement on Monday that "a further person died in an Australian hospital last night as a result of injuries suffered in the Whakaari/White Island eruption".
Another 13 people remain in hospital in New Zealand, where 16 of the official deaths have been recorded.
Two people not listed in the official toll were still missing in the waters around Whakaari/White Island, and presumed dead.
On December 24, 2019, New Zealand authorities called off the search for missing New Zealand tour guide Hayden Marshall-Inman, 40, and Australian Winona Langford, 17, a week after the search had been scaled back due to no items of significance being found.
The New Zealand authorities have opened two investigations to look into the incident on the privately-owned island.
In total, 47 people - 24 Austral, nine Americans, five New Zealanders, four Germans, two Britons, two Chinese and a Malaysian citizen - were on the island when the volcano erupted on December 9, 2019.
The 321-metre-high, Whakaari/White Island, 70 per cent of which is below sea level, is one of New Zealand's most active volcanoes and a popular tourist attraction.
In 2018 it was visited by more than 17,500 people.
Located at the southeastern end of the Ring of Fire, Whakaari last erupted in 2016 without causing fatalities.
The deadliest incident at the site occurred in 1914 when 10 miners died as a result of a landslide caused by the collapse of part of the volcano's crater.
( With inputs from IANS )