“We currently have 11 people dead and more than 100 injured, several of whom have been hospitalised… rescue operations are ongoing,” Augustine Ollomi, the Kagera province police chief in charge of the Bukoba district said by telephone.
Residents of the Tanzanian town of Bukoba, near the epicentre, had earlier told AFP that some houses there had caved in.
The earthquake measured 5.7 and was felt in nearby Rwanda, Burundi, Uganda and Kenya, the US Geological Survey said.
The epicentre of the 1227 GMT quake was about 25 kilometres (15 miles) east of the north-western town of Nsunga on the border of Lake Victoria.
“The walls of my home shook as well as the fridge and the cupboards,” also said an AFP correspondent in the Ugandan capital Kampala.
Earthquakes are fairly common in the Great Lakes region but are almost always of low intensity.