The report says Ethiopia has cut the number of child deaths to 68 per 1,000 births from more than 200 in 1990.
The government attributed the improved figures to its growing economy.
Despite the reduction, the UN Children's Fund said Ethiopia needed to do much more to improve health facilities for pregnant women.
Ethiopia is one of Africa's poorest states, although it has experienced rapid economic growth in recent years and is one of the continent's leading coffee producers.
Its economy revolves around agriculture, which in turn relies on rainfall.
The BBC's Emmanuel Igunza in the capital, Addis Ababa, says Ethiopia was once a byword for malnutrition in Africa.
But the latest Unicef figures show Ethiopia is one of the few African countries on the path to realising the millennium development goal of reducing child mortality rates, he says.
Ethiopia's Health Minister Kesetebirhan Admasu said increasing household incomes had helped improve people's health.
"This has also resulted in better nutrition for children [and] women; this has translated into better sanitation - all these have direct or indirect impact on the survival of children," he told BBC Africa.
He said the government has also been "aggressively expanding its primary healthcare network".
"We have now 93% coverage of one health centre for 25,000 people, which basically means one health facility within a 7km (four mile) radius," he said.
Ethiopia has more than halved its mortality rates for children under the age of five years during the last two decades, new UN statistics show.