The offshore temblor’s epicenter was about 69 kilometers north of the province’s Borongan town, said the Philippine Institute of Volcanology and Seismology (Phivolcs).
The earthquake, which struck at 1:14 a.m., was felt as far away as Surigao City, some 300 kilometers from the epicenter.
Phivolcs said damage and strong aftershocks could be expected but that it had not confirmed any so far.
Neri Amparo, chief of the operations center of the Office of Civil Defense, said a five-year-old boy, identified as Marvin Lequim, was killed and a four-room elementary school building collapsed in the remote coastal town of Can-avid.
Local disaster officer Luisito Moscosa said the town’s public market also collapsed, electric posts fell and roads cracked.
A landslide blocked a mountainside highway in nearby Taft town.
Can-avid Mayor Norman Germino said the five-year-old boy was killed after being pinned by a collapsed wall.
Several residents also sustained minor injuries due to debris from collapsed walls and destroyed appliances.
"Sixty percent of the 2,000 households in the poblacion (town proper) were damaged," Germino said.
Power supply to the town, as well as other areas of Eastern Samar, has been cut and a local telephone company was one of few establishments with a generator.
"We were awakened from our sleep by a sudden jolt. It felt like something was boiling and we were being rocked," said Helen Adan, a telephone operator from Can-avid.
She added that on her way to work, she saw several damaged houses.
Amparo said residents along coastal areas were evacuated to higher ground but that no tsunami, or tidal wave, was reported. Officials were assessing the damage, she added.
The Philippines is along the Pacific "Ring of Fire," where earthquakes and volcanic activities are common.
A magnitude 7.7 earthquake in 1990 killed nearly 2,000 people on the main island of Luzon. — Miriam Garcia Desacada, Felix de los Santos and wire reports