"The expected period of significant tsunami waves is now over for all threatened Indian coastal areas," said a bulletin from the national tsunami early warning centre in the southern Indian city of Hyderabad.
The top-level warning issued for India's Andaman and Nicobar Islands, which lie north of Indonesia in the Bay of Bengal, was downgraded to a precautionary alert.
In Sri Lanka, where some 30,000 people perished in the 2004 disaster, the state Disaster Management Centre said they had also withdrawn their tsunami warning.
"Return to usual places of residence," it said in a statement that cancelled the alert in line with advice from the US Pacific Tsunami Warning Center.
The quake hit 431 kilometres (268 miles) off the Indonesian city of Banda Aceh at 0838 GMT, and was followed by another undersea quake measured at 8.2, the US Geological Survey said.
India responded by issuing immediate alerts for a number of its southern and eastern coastal states, including West Bengal, Tamil Nadu and Andhra Pradesh, as well as the tourist states of Kerala and Goa on the west coast.
Tremors were felt in the Indian eastern city of Kolkata, where cracks appeared in some tall buildings.
A large number of people rushed out of offices in the city's central Park street area as windows and doors rattled.
Residents in multi-storeyed buildings also fled to open areas, and metro passengers were evacuated from stations and rail services were suspended.
Fishermen in West Bengal were also asked not to venture out to sea.
In the high-tech hub of Bangalore, mild tremors lasting about 10-15 seconds were felt, causing widespread panic.
Several hundred people were evacuated from their homes in the Andaman and Nicobar islands, 1,600 kilometres (990 miles) from the Indian mainland.
"All the administration officials have been asked to move out from the region. This is not an evacuation but just a precautionary step," said the islands' chief secretary Shakti Sinha.
The islands -- a number of which are home to indigenous tribes and not open to tourists -- were badly hit by the 2004 tsunami, which destroyed homes, schools and hospitals and left 454 people dead and thousands missing.
India has conducted a number of tsunami drills since the 2004 disaster killed 16,000 people.
The worst hit area was the poverty-stricken fishing district of Nagapattinam in Tamil Nadu, where around 6,500 people perished along a narrow strip of coast.
Tens of thousands of poor Indians lost their flimsy homes in the disaster, which prompted a massive relief effort by Indian authorities.