The accident took place in the Bona district, according to a statement from the Sidama regional government.
Wosenyeleh Simion, spokesperson for the Sidama government, confirmed to Reuters on Monday that the death toll had risen to 71.
"Five are in critical condition and receiving treatment at Bona General Hospital," he added.
Earlier, the regional communication bureau reported the death toll as 60 in a statement issued on Sunday.
Wosenyeleh explained that the truck missed a bridge and fell into a river, noting that the road had many sharp bends.
Some of the passengers were returning from a wedding ceremony, and several families lost multiple members in the crash.
Traffic police in the region indicated that the truck was overloaded, a factor likely contributing to the accident.
The state-run Ethiopian Broadcasting Corporation (EBC) also reported that the passengers were on their way to a wedding when the incident occurred.
Fatal traffic accidents are common in Ethiopia, where driving standards are often poor, and many vehicles are in substandard condition.
In 2018, at least 38 people, mostly students, died when a bus plunged into a ravine in the northern part of the country.