Air Senegal flight HC 301 bound for Bamako, the capital of Mali, ran off the runway in the early hours of Thursday, Dakar’s Blaise Diagne Airport said in a statement.
The pilot was slightly injured, but most of the 78 passengers on board were not injured in the incident.
Operations at the airport have since been suspended.
Emergency services at the airport were mobilized to evacuate the passengers, the airport statement said.
An investigation is underway to determine the cause of the incident, which occurred around 01:00 GMT.
Boeing did not comment on the incident, nor did Transair, the private company from which Air Senegal leased the plane.
While the cause of the crash is not yet known, it comes as the manufacturer faces a deepening crisis over its safety record.
What trouble is Boeing in?
An unused door exploded on an Alaska Airlines Boeing 737 Max in January shortly after takeoff from the US.
The company is facing a criminal investigation into that incident.
The accident in Senegal comes as a former quality inspector at Boeing’s biggest supplier told the BBC that plane bodies regularly left the factory with serious defects.
The company, Spirit AeroSystems, said it “totally disagrees” with the allegations.
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