People have been evacuated from Barren Island since the eruption began Tuesday night and there were no reports of injury.
Lava was flowing out of the rim of the crater which towers above the Indian Ocean some 500 metres (yards) away, the sources said.
Tourists used to visit by boat and the island has a police station.
The volcano, known as Barren 1, is located some 135 kilometres (80 miles) northeast of the capital Port Blair, and last erupted in 1996.
It runs about 150 fathoms deep under the sea and usually gives off smoke.
M.M. Mukherjee of the Geological Survey of India told AFP the volcano presents little real danger.
"The risk is minimised because it is surrounded by the sea so if at all there is a lava flow it will roll off into the sea," he said.
The Andamans has reported a series of major aftershocks daily since Sunday's massive undersea quake off Sumatra.
The Andaman and Nicobar Islands are located near a zone of intense tectonic activity.
A second volcano, called Narcondam and considered dormant, lies close to Barren Island, which also erupted in 1991 after more than a century of inactivity.