It was the second crash in five months involving a 737 Max 8, the newest version of the plane.
Comparisons are being drawn with a Lion Air accident last October where the plane lost altitude soon after takeoff.
However, experts warn it is too early to say what caused the Ethiopian Airlines disaster.
Ethiopian Airlines says the plane, flight ET302, crashed at 08:44 local time (05:44 GMT), just six minutes after it left Addis Ababa. The aircraft, bound for Nairobi, came down near the town of Bishoftu, 60km (37 miles) south-east of the capital.
The pilot had reported difficulties and had asked to return to Addis Ababa, the airline said.
"At this stage, we cannot rule out anything," Ethiopian Airlines CEO Tewolde Gebremariam told reporters at Bole International Airport in the capital.
Passengers from more than 30 countries were on board the flight, including 32 Kenyans, 18 Canadians, and seven Britons.
At least 19 victims were affiliated with the United Nations, according a UN official.
Slovak MP Anton Hrnko also confirmed via Facebook that his wife and two children were on the plane.
In response to the accident, Ethiopia has declared Monday a national day of mourning.