The US Geological Survey (USGS) said on its website that a 6.8-magnitude earthquake struck at just before 2.30pm (1219 GMT) in a region it named as Congo-Tanzania.
The epicentre was 55km southeast of the town of Kalemie in the Democratic Republic of Congo, it said.
Hundreds of people evacuated office buildings in the centre of Nairobi, Kenya, after the earth shook and waited for any information about what was going on.
Andrzej Kijko, head of seismology unit at South Africa’s Council for Geoscience, said: “A quake of this kind could easily produce significant damage, but I wonder what kind of infrastructure they have there in the region. There may not have been much to destroy.”
The earthquake was also felt in the Rwandan capital, Kigali, which lies directly north on a USGS map, and by residents in Burundi’s capital, Bujumbura.
Simeon Nduwimana, a taxi driver, said: “We felt the ground shake.”
But he said the situation was now normal and he had not seen any buildings damaged.
The East African Rift System is a 60km-wide zone of active volcanics and faulting that runs from north to south in eastern Africa for more than 3000km from Ethiopia in the north to Zambezi in the south.
It is a rare example of an active continental rift zone, where a continental plate is attempting to split into two plates which are moving away from one another.