The aircraft, carrying passengers from 33 countries, was only months old and of the same type involved in a previous disaster.
The state-owned carrier has confirmed there were no survivors from Flight ET 302, carrying 149 passengers from 33 countries and eight crew members.
The Boeing 737-8 MAX was on a regular scheduled flight to Nairobi in Kenya, when it came down shortly after taking off from the Ethiopian capital, Addis Ababa.
The plane "had an unstable vertical speed" after take-off, according to the flight tracking website Flightradar24.
Kenya's transport secretary James Macharia described the crash as a "regrettable incident".
He said Kenyan authorities were trying to find out exactly what happened, but because the plane came down in Ethiopian airspace they had limited information.
Mr Macharia told reporters: "It is a very sensitive emotional matter.
"We are waiting for more information to come from Ethiopian Airlines.
"What we are doing ourselves is to provide as much support as possible to relatives and friends waiting to meet passengers."
He said they would be taken to a hotel at Nairobi airport where an emergency centre had been set up to provide them with support and assistance.
Among the relatives at Nairobi airport was Wendy Otieno, clutching her phone and weeping.
She said: "We're just waiting for my mum. We're just hoping she took a different flight or was delayed. She's not picking up her phone."
The aircraft is just a few months old, having taken its first flight at the end of October.
It is the same type as the Lion Air plane which crashed into the see off Indonesia last year killing all 189 on board.
In the wake of that disaster Boeing issued a warning to airlines using its 737 MAX planes after a sensor failure was identified as a potential cause of the crash.
Office of the Prime Minister - Ethiopia
The Office of the PM, on behalf of the Government and people of Ethiopia, would like to express it’s deepest condolences to the families of those that have lost their loved ones on Ethiopian Airlines Boeing 737 on regular scheduled flight to Nairobi, Kenya this morning.
8:50 AM - Mar 10, 2019
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Ethiopian Airlines said in a statement that it "deeply regrets the fatal accident".
It added: "The group CEO who is at the accident scene right now regrets to confirm that there are no survivors.
"He expresses his profound sympathy and condolences to the families and loved ones of passengers and crew who lost their lives in this tragic accident."
The airline, which changed its Twitter account cover photo to black following the disaster, has posted emergency numbers to call.
The Ethiopian prime minister's office has offered condolences to families.
Boeing said it was "deeply saddened" at the tragedy.
It said in a statement: "We extend our heartfelt sympathies to the families and loved ones of the passengers and crew on board and stand ready to support the Ethiopian Airlines team.
"A Boeing technical team is prepared to provide technical assistance at the request and under the direction of the US National Transportation Safety Board."