The inferno, which raged from Tuesday midnight to Wednesday morning, destroyed goods and properties worth millions.
A 65-year-old man was said to have died in the incident which is suspected to be the handiwork of arsonists.
Speaking during a visit to the market on Wednesday, the Lagos governor said the state government would get to the bottom of the matter.
“In strong terms, I am directing the commissioner of police to immediately launch a full investigation into the cause of this incident. Given the issues we are hearing around, I am also directing the commissioner to tighten security around markets. All vulnerable markets must be protected.
“People must not jump into conclusions as to the motives behind it, because this is an incident that affects everyone around this neighbourhood in one form or the other. We have received the list of all shop owners affected and we will vet the list for compensation to help the victims back on their feet.”
Meanwhile, President Muhammadu Buhari has expressed his “deepest sympathies” with the traders and their families.
“The president is equally concerned that a similar fire incident occurred at the popular Balogun market a few weeks ago, calling on relevant authorities to take precautions to stem the tide,” Garba Shehu, presidential spokesperson, quoted Buhari as saying.
The president commended the Lagos State Fire Service for salvaging a nearby filling station with a 33,000 litres PMS tanker and other properties in the area.