The aircraft, operated by Nigeria's Associated Airlines, came down in open ground, close to an aviation fuel depot in the commercial capital.
Local media reported it was carrying the body of a former regional governor, and members of his family, to his funeral. A Reuters reporter saw emergency workers take a coffin out of the wreckage.
"The plane was making a lot of noise before it came down," Rasheed Olajide, an engineer at the airport, told Reuters.
The aircraft appeared to make a maneuver to avoid a residential area, he added.
The Embraer 120 plane, a Brazilian make, was flying to Akure, a town about 140 miles east of Lagos, and came down just after 9:30 a.m. (4:30 a.m. ET), Aviation Minister Stella Oduah said in a statement.
The plane's flight recorder had been found and an investigation started into what caused the crash, she added.
Sixteen people were killed and four survived, said Usman Muktar, Commissioner of the Accident Investigation and Prevention Bureau.
A diplomatic source told Reuters the engine was made by Pratt & Whitney Canada, a unit of United Technologies Corp, PW100.
According to the airfleets.net website, which keeps a record of passenger aircraft worldwide, the crashed aircraft was more than 23 years old.
Embraer said it had offered to help authorities investigate the crash of the 30-seater plane.
Africa's second largest economy has seen a series of air accidents.
In June last year, 163 people died when a Dana Air plane crashed into a Lagos apartment block in the country's worst airline disaster in two decades.