The Associated Airlines plane took off at about 9:30 (local time) from the domestic terminal at Lagos's Murtala Mohammed International Airport with 13 passengers and seven crew on board.
At least 13 people died while six others were injured after the plane nosedived into the ground near an aviation fuel depot, Joe Obi, the spokesman of the country's aviation ministry, said. However, officials put the death toll at 14.
Airport officials said the plane suffered engine failure few minutes after taking off and descended into the fuel depot but narrowly missed the fuel-laden containers. The Brazilian-made turboprop Embraer-120 plane was bound for the capital of Ondo state, Akure, about 225km north-east of Lagos.
It was carrying mourners and the body of the former state governor, Olusegun Agagu, who was to have been buried this weekend. The aircraft's black box has been recovered while the remains of the late governor has been taken to an air force base, airport sources were quoted as saying by local radio station Inspiration FM.
Officials: Plane suffered engine failure minutes after take off
"I heard a loud bang and then there was lots of black smoke. The security forces rushed straight to the scene. I saw three bodies removed from the wreckage," eyewitness Ahmad Safian told the BBC.
He said the road to the airport was blocked for a short time but operations were continuing as normal at the airport. Barely a year ago, a plane owned by an Indian businessman, Dana Air crashed as it approached Lagos from Abuja, killing 153 people on board and six others on the ground.