Some scavengers tried to remove the doors on the ground floor, when the remaining part of the building collapsed on them.
Four people have been rescued from the rubble of the building, which collapsed on Monday in Lagos.
The incident occurred at 57, Egerton Square, Oke Arin, Lagos Island.
The building had been marked by the Lagos State Building Control Agency (LSBCA) for demolition, which began on Sunday.
According to the Lagos State Emergency Management Agency (LASEMA), the officials were on top of the building when some scavengers tried to remove the doors on the ground floor and the remaining part of the building collapsed on them.
The four scavengers sustained minor injuries and were taken to the hospital.
Rasaki Musbau, the Director of the Lagos State Fire Service, said: "Information from our men on the ground at the scene showed that it was a partial collapse. They have removed four persons trapped in the building. They are all alive."