Two pilots fell asleep at 37,000ft (11,000m), missing an airport runway before waking to safely land the plane, an aviation publication says.
Air traffic tried to contact them after they overshot the point of descent into Ethiopia's Addis Ababa airport.
The pilots eventually woke up and landed the plane on its second approach, the Aviation Herald said.
The Ethiopian Airlines crew have been put on leave pending investigation, state-run news outlet Fana reported.
Monday's passenger flight took off from Sudan's Khartoum airport.
The Boeing 737, with a 154-seat capacity, normally takes less than two hours on its route between the neighbouring countries.
Reactions to sleeping on the job ranged from sympathy with the pilots' work schedule to shock that they fell asleep on the job.
"I wouldn't cast blame on the Ethiopian crew specifically here - this is something that could happen to ANY crew in the world and it probably DID happen... The blame lies on the corporation and the regulators," read one comment on the Aviation Herald website.
Another user suggested that there was only one solution: "Termination. End of story. Full stop."
Others saw the funny side of the story, comment on Twitter, "Sleeping on the job taken to new heights!"
An aviation analyst called the incident "deeply concerning" on Twitter.
"Pilot fatigue is nothing new, and continues to pose one of the most significant threats to air safety - internationally," tweeted aviation analyst, Alex Macheras.
The BBC has contacted Ethiopian Airlines for comment.
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