There have been no immediate reports of the number of people on board the aircraft.
“We are still relying on eye witness accounts, which say they saw the plane plunge into the ocean,” Lagos State health commissioner Leke Pitan told AFP on Lekki Beach, 20 kilometres (13 miles) outside the city.
“We’re talking now of a recovery operation, and not a rescue operation because if indeed a plane plunged, there’s nothing to rescue. This happened four hours ago,” he said, putting the time of the reported crash at around 3:00 pm (1400 GMT).
But he added: “We’ve yet to get confirmation of the plane actually plunging.”
Security officials told AFP that the plane was thought to be a light 25-seater aircraft. Police and Red Cross rescue teams were deployed to the scene, but could not immediately locate any wreckage or survivors.
An official in the office of Aviation Minister Isa Yuguda said the minister had gone to Lagos airport to meet with aviation officials on the incident, but no more details were available.
Several private firms rent charter small aircraft to Nigerian and international companies, including the foreign oil majors who operate the west African country’s large oil industry.