The Malawi quake, which occurred at 1.19am local time (2319 GMT) and was 15.2km deep, was the latest in a series of tremors in the uranium-rich Karonga district this month.
A four-year-old boy and two adults were killed and up to 250 people injured on Sunday when a 6.0 magnitude earthquake destroyed buildings in Malawi's northern district of Karonga.
A local government official called on thousands of people to leave their homes because of damage to buildings and the threat of further tremors.
Another tremor struck neighbouring Tanzania, according to the US Geological Survey (USGS), but initial reports said there was no serious damage or injuries.
The Malawi quake, which occurred at 1.19am (2319 GMT Saturday) at a depth of 9.4 miles (15.2km), was the latest in a series in the uranium-rich Karonga district this month. A one-year-old child was killed on December 8.
"Two people have died, a four-year-old child and his grandmother, after the house they were sleeping in collapsed on them," police spokesman Enock Livasoni told Reuters.
Another man died in hospital as a result of head injuries, said nurse who declined to be identified.
She said up to 250 people appeared to have been injured, but no other patients were in critical condition.
Livasoni said damage to villages was extensive, with many schools and government buildings affected.
Karonga District Assembly chief executive Gasten Macheka said about 270,000 people had been urged to leave their homes.
"We are asking everyone in Karonga not to be in houses or near houses because the situation is unstable," he was quoted as saying by the South African news agency SAPA.
He appealed for government help and international assistance in providing tents and medical supplies.
About 3,000 Malawians live in makeshift shelters as a result of damage to their homes from previous quakes.
Production at Australian Paladin Energy's, Kayelekera uranium mine was not affected.
"The mine is designed to withstand earth movements greater than what is the current range," Paladin spokesman Neville Huxman told Reuters.
In 1989, a 6.6 magnitude earthquake killed at least nine people and injured 100 in central Malawi and made 50,000 homeless, according to the USGS.
The Tanzanian quake, of 6.2 magnitude, occurred 84 miles (135km) south of the town of Mbeya, at a depth of 6.2 miles (10km).
"Up to now, there are still no reports of damage or injury. It was in Kyera district and Mbeya. You could feel the tremors but no buildings fell down," said the regional police commander of Mbeya, Advocate Nyombi.
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