Two people, including a child, died in Sikkim state, the epicentre of the earthquake, and two others died in Bihar state in a stampede sparked by the quake, CNN-IBN broadcaster said.
Sikkim is prone to landslides and many high-rise buildings have sprung up in its mountain towns over the last few years of economic boom. There were concerns the toll could rise as information arrived from remote areas.
"The reports of casualties so far has been low. But we don't have a true picture yet as there is blackout and communications are down in many places," Mrinal Gohain, ActionAid's manager for the northeast, told Reuters by phone from Guwahati, the main city in Assam state.
Sikkim is India's most sparsely populated state, located in the Himalayas between Nepal, Bhutan and Tibet.
In neighbouring Nepal, at least five people died, Deputy Prime Minister Narayan Kaji Shrestha told reporters after a cabinet meeting. Police said at least 61 people were injured.
Several buildings collapsed in Sikkim's capital Gangtok, and widespread power cuts were reported across the northeastern state, television channels said.
There were also reports of landslides in Sikkim and West Bengal state. Several Indian Air Force jets with personnel and equipment were immediately dispatched to Sikkim.
The U.S. Geological Survey said on its website the quake was centered 64 km (40 miles) north west of Gangtok, capital of Sikkim. It was 10 km (6.2 miles) deep.
"Cracks have developed in some buildings in Gangtok. Most phone lines are down and there is no electricity now. People have come out on the street," said Gangtok resident Bobby Dahal.
"It is too early to ascertain any damage. We are trying to get in touch with the state government of Sikkim to know if they need any help from us," Sujata Saunail, joint secretary of he National Disaster Management Authority, told Reuters.
The quake was felt all the way to Bangladesh, shaking buildings in the capital and neighbouring areas. At least 10 people were injured and some buildings suffered minor damage.
Thousands of panic-stricken families in Dhaka ran out of high-rise buildings on to the streets as the ground under their feet shook.
"I never experiences such a dreadful moment in my life. Suddenly lights went off and there was people running and crying around," said Shamsul Islam, a 70-year-old man in Chittagong port city in Bangladesh.
Several earthquakes have hit north and east India this year, but none have caused major damage or injuries.