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 has been put on leave pending an 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 neighboring countries.
Reactions to sleeping on the job ranged from sympathy with the pilots' work schedule to shock that they fell asleep on the job.
In a press release, Ethiopian Airlines confirmed that the crew had been removed from future flights pending further investigation.
"Appropriate corrective action will be taken based on the outcome of the investigation" the statement read.
"Safety has always been and will continue to be our first priority."