The US Geological Survey (USGS) reported that a 6.8-magnitude quake struck near the town of Kalemie in the Democratic Republic of Congo at 1219 GMT on Monday, 975km southwest of the Kenyan capital Nairobi.
Besides Kenya and Congo, tremors were also felt in Burundi, Rwanda and Tanzania, impoverished countries connected by a string of lakes and mountains, many of them active volcanoes.
Residents of Kalemie, an eastern Congolese town on the shores of Lake Tanganyika with a population of 200,000, reported at least one death and several injuries and said mud-brick houses had collapsed in poor neighbourhoods.
Fidel Muteba, community leader in Kalemie, said: "A child died when the house he was in collapsed during the earthquake. Several other people have broken limbs and are in hospital. We'll see in the hours that come if more come to hospitals."
It was the first fatal seismic event in the region since 2002 when Africa's deadliest eruption in 25 years swept away thousands of homes and killed 25 people after the 3469m Mount Nyiragongo exploded near the town of Goma in eastern Congo.
Hundreds of people fled office buildings in the centre of Nairobi on Monday after the tremors and the streets were clogged with people trying to drive away from the city centre.
Tabitha Nyambati, an office worker, said:
"People came running down, scared, because you don't know what it is. You're moving this way and that."
Peter Ragula, 37, a salesman, said: "We actually saw the building shaking and seats moving in the building.
"People were saying they were dying … I thought I was sick at first, I thought I was very dizzy, but I realised seats were moving and I realised there must have been a problem."
Tremors in Tanzania
Officials in Tanzania said the tremor was felt there but that they had received no reports of any injuries.
Abdalah Mssika, regional police commander for the Shinyanga region bordering Lake Victoria, said: "We felt a tremor at about 3.20pm, but that is all we've had. I have no reports on injuries or damages in my region."
The quake was also felt in Kigali, the Rwandan capital, and by residents in Burundi's capital of Bujumbura.
"People were saying they were dying … I thought I was sick at first, I thought I was very dizzy, but I realised seats were moving and I realised there must have been a problem"
salesman in Nairobi
Simeon Nduwimana, a taxi driver in Bujumbura, said: "We felt the ground shake." He said that the situation was now normal and he had not seen any damaged buildings.
In Kigali, Abdul Hamidou, who works in an internet cafe, said: "The desktop screens were moving, my chair was shaking making me feel dizzy, and all of a sudden I saw customers running out."
Africa's most active volcanoes are in the Rift Valley, which runs north to south for 5000km along the earth's crust from northern Syria to central Mozambique.