The Air Senegal plane bound for the Malian capital Bamako went off the runway in the early hours of Thursday, Dakar's Blaise Diagne airport said in a statement.
Though it is not yet known what caused the crash, it comes as the manufacturer faces a deepening crisis over its safety record.
The Senegal crash comes as a former quality inspector at Boeing's largest supplier told the BBC that plane bodies regularly left the factory with serious defects.