"Search and rescue operations are in progress and we have no confirmed information about survivors or any possible casualties," the airline said in a statement.
The flight had unstable vertical speed after take off, said flight tracking website Flightradar24 on its Twitter feed.
At Nairobi airport, many passengers were waiting at the gate, with no information from airport authorities.
"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," said Wendy Otieno, clutching her phone and weeping.
Robert Mudanta, 46, was waiting for his brother-in-law coming from Canada.
"No, we haven't seen anyone from the airline or the airport," he told Reuters at 1pm, more than three hours after the flight was lost. "Nobody has told us anything, we are just standing here hoping for the best."
The Ethiopian prime minister's office sent condolences via Twitter to the families of those lost in the crash.
On Oct. 29, a Lion Air Boeing 737 MAX 8 crashed into the Java Sea shortly after take-off from Jakarta, killing all 189 people on board.
The plane is the latest version of the 737 family, the world’s best selling modern passenger aircraft and one of the industry’s most reliable.
State-owned Ethiopian is one of the biggest carriers on the continent by fleet size. It said previously that it expected to carry 10.6 million passengers last year.
Its last major crash was in January 2010, when a flight from Beirut went down shortly after take-off.
"There are no survivors onboard the flight, which carried passengers from 33 countries," said state-run Ethiopian Broadcasting Corporation, quoting an unidentified source at the airline.