More than 50 people were injured in the blaze, which broke out in the middle of the night destroying many properties.
The Gikomba is one of the largest open-air markets in the city and fires there are frequent, leading to speculation about possible arson attacks, The Standard newspaper says.
However, the cause of the current fire is not known.
Some of the victims were burned while others inhaled poisonous fumes as they tried to salvage their property.
Pictures from Reuters news agency showed people searching the wreckage and ash.
The injured have been rushed to different hospitals across the city.