The security guard fell to his death after Argentina's win over the Netherlands in the World Cup.
John Njau Kibue died three days after being admitted to the hospital.
The circumstances of the fall are being investigated by the organizers.
The 24-year-old's sister told CNN they have not been given an explanation.
We want to be treated fairly. He died and we want to know what happened. Ann Wanjiru said that they have never received a picture of where he fell from.
His family told CNN that he moved to Qatar to work for a security firm.
Kibue is the second migrant worker reported to have died since the start of the World Cup on 20 November. A Filipino national fell to his death while carrying out repairs at a resort used as a training base by the Saudi Arabian team, The Athletic reported.
The tournament's supreme committee offered "sincere sympathies" to Kibue's family and friends.
According to a report by the Guardian newspaper, 6,500 migrant workers have died in the country since it hosted the World Cup.
There have been three work related deaths in construction related to the tournament, according to the authorities. The figure increases to between 400 and 500 when infrastructure projects are included.