The plane took off at 8:38am (05:38 GMT) from Bole International Airport and "lost contact" six minutes later.
At 6:22 p.m. Jakarta time, United States company Boeing confirmed that the aircraft was a Boeing 737-MAX 8, the same aircraft that was used for Lion Air flight JT610, which crashed in Indonesia in late October.
As sunset approached, crews were still searching for the plane's flight-data recorder, the airline's chief operating officer said.
Under global rules, responsibility for leading the crash investigation lies with Ethiopian authorities, while the US National Transportation Safety Board (NTSB) will automatically take part because the Boeing aircraft was designed and built in the United States.
The flight had unstable vertical speed after takeoff, said flight-tracking website Flightradar24 on its Twitter feed.
Records show that the plane was new.
The state-owned Ethiopian Airlines, widely considered the best-managed airline in Africa, calls itself Africa's largest carrier and has ambitions of becoming the gateway to the continent.
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The aircraft, flight number ET 302, went down near Bishoftu, southeast of Addis Ababa.
People from 33 countries were on board, of which 32 were Kenyans and 17 Ethiopians.
Eight Chinese passengers were on board, said Li Liang, spokesperson for the Chinese Embassy to Ethiopia.
The crash shattered more than two years of relative calm in African skies, where travel had always been chaotic.
In December 2018, CNBC expected Africa to remain the weakest airline region in the world for 2019, where it has been ranked for the past four years. The Ethiopian Airlines plane was "brand new" and had been delivered to the airline in November, GebreMariam said. ET-AVJ had over 1,000 hours with the airline since delivery.
Boeing said a technical team was ready to provide assistance at the request of the U.S. National Transportation Safety Board.
Its last major accident occurred in 2010 when it crashed into the Mediterranean shortly after takeoff from Beirut, killing all 90 people on board.
In Addis Ababa, members of an association of Ethiopian airline pilots wept uncontrollably for their dead colleagues. The flight has crashed 60km south-east of the airport.