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.
Visibility was said to be good but air traffic monitor Flightradar24 reported that the plane’s “vertical speed was unstable after take-off”.
The pilot was named as Senior Captain Yared Getachew who had a “commendable performance” with more than 8,000 hours in the air, the airline said.
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 to a UN official.
Some passengers were heading to a session of the UN Environment Assembly in Nairobi which began with a minute’s silence on Monday.
Slovak MP Anton Hrnko also confirmed via Facebook that his wife and two children were on the plane.
Meanwhile, a Greek man has said that he was due to board the flight but arrived at the gate two minutes late.
In a Facebook post, Antonis Mavropoulos shared an image of his ticket and said it was his “lucky day”.
“I was angry because nobody helped me to reach the gate on time,” he wrote. “I’m grateful to be alive.”
In Ethiopia, Monday has been declared as a national day of mourning.