The flight is believed to have had 149 passengers and eight crew members on board, the airline says.
A spokesman said the crash happened at 08.44 local time on Sunday, shortly after take-off from the Ethiopian capital.
First word of the crash came when Prime Minister Abiy Ahmed expressed his “deepest condolences” on Twitter.
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.
In a statement, the airline said that search and rescue operations were under way near the crash site around the town of Bishoftu, which is 60km (37 miles) south-east of the capital.
It did not provide details on the number of casualties. It is not clear what caused the crash.
“Ethiopian Airlines staff will be sent to the accident scene and will do everything possible to assist the emergency services,” the statement added.
Boeing, the company that built the aeroplane, said in a tweet that it was “closely monitoring the situation”.
Its 737 Max-8 aircraft is relatively new to the skies, having been launched in 2016. It was added to the Ethiopian Airlines fleet late last year.
Another plane of the same model was involved in a crash five months ago, when a Lion Air flight crashed into the sea near Indonesia with nearly 190 people on board.
What do we know about the airline’s safety record?
Ethiopian Airlines flies to many destinations in Africa, making it a popular carrier in a continent where many airlines fly only from their home country to destinations outside Africa.
It has a good reputation for safety, although in 2010 one of the company’s aeroplanes crashed in the Mediterranean Sea shortly after leaving Beirut.
The incident killed 90 people on board.
The airline’s highest fatalities to date came in a November 1996 crash during a hijacking on a flight from Addis Ababa to Nairobi.
One of the aeroplane’s engines stopped when the fuel ran out and although pilots attempted an emergency water landing, they hit a coral reef in the Indian Ocean and 123 of the 175 people on board were killed.