John Njau Kibue, 24, suffered critical injuries in the early hours of Saturday, hours after Argentina beat the Netherlands in the quarter-finals.
"We regret to announce that, despite the efforts of his medical team, he sadly passed away in hospital on Tuesday 13 December, after being in the intensive care unit for three days."
"Stadium medical teams immediately attended the scene and provided emergency treatment before he was transferred to Hamad Medical Hospital's intensive care unit," said an organizing committee spokesperson.
Kibue's family in Kenya has been told, said the spokesperson, who added: "We send our sincere condolences to his family, colleagues and friends during this difficult time."
Organizers are "investigating the circumstances leading to the fall as a matter of urgency and will provide further information pending the outcome of the investigation.
"We will also ensure that his family receive all outstanding dues and monies owed."
Organisers had said before the latest fatality that there had been 37 deaths of World Cup workers, but only three involving "work-related" accidents.
Rights groups have said thousands of foreign migrant workers have died on construction projects across Qatar over the past decade and demanded that football's world governing body FIFA and the government launch a special compensation fund.
The government has said its existing fund has already paid out more than $350 million and would handle any future claims.