"We have not issued any tsunami warning so far and there is no need for widespread evacuation required because it's 6.3. We are studying the situation." The islands lie about 1,200 km (750 miles) off India's east coast.
The US Geological Survey said the quake was magnitude 6.7 and occurred at 1140 GMT. It was centred 71 miles (114 km) southwest of Port Blair, capital of the Andaman Islands, and was 21.7 miles (35 km) deep.
USGS later said an aftershock of 6.1 magnitude and 30 km deep struck at 1307 GMT. The epicentre was under the seabed near the location of the earlier quake.
Hundreds of people were out on the roads in Port Blair, officials and witnesses said. People ran out of their houses and telephone lines were jammed.
"There is no news of loss of life or property till now," said Casper James, a senior disaster management official in the islands.
Police were asking people not to panic and return to their homes.
"Everything in my office started to shake and we ran out as fast as possible," said Kumar Avinash, a local resident.
(Reporting by Krittivas Mukherjee; Additional reporting by Sanjib Kumar Roy in Port Blair; Editing by Alistair Scrutton and David Fogarty)